Maths-
General
Easy
Question
If
, then
![k equals 0 comma K equals pi](data:image/png;base64,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)
![k equals 0 comma K equals pi divided by 2](data:image/png;base64,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)
![k equals pi divided by 2 comma K equals pi](data:image/png;base64,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)
- None of these
Hint:
In this question, we have to find the k and K, we have given k ≤ sin-1x + cos-1x + tan-1x ≤ K. Here, it is asking about the period of this function.
The correct answer is: ![k equals 0 comma K equals pi](data:image/png;base64,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)
Here we have to find the range of function which , k and K.
Firstly, we have k ≤ sin-1x+ cos-1x +tan-1x ≤ K
We can write,
sin-1x + cos-1x + tan-1x =
+ tan-1x [we know sin-1x + cos-1x =
]
since,
k ≤
+ tan-1x ≤ K
so , sin-1x and cos-1x only defined if -1 ≤ x ≤ 1
we know that,
(
) ≤ tan-1x ≤(
)
(
) ≤
+ tan-1x ≤(
)
(
) ≤
+ tan-1x ≤(
)
Therefore, k =
and K = ![fraction numerator 3 straight pi over denominator 4 end fraction](data:image/png;base64,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)
The correct answer is None of these.
In this question, we have to find the range of function from k to K. Here we know that sin-1x + cos-1x = and it only defines if -1 ≤ x ≤ 1 . And tan^-1x lines in (
) to (
) .
Related Questions to study
physics-
In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in figure. The value of the unknown mass m is :–
![](data:image/png;base64,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)
In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in figure. The value of the unknown mass m is :–
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeQAAABiCAYAAACBMKCIAAAabUlEQVR4nO3dZ1gUVxsG4GdBpFkBAY2gsQAqGkWwAIqiYC/R2DWJn0mMGmMs2LGb2EBFEzWWxBgL9hbFhhojAlIFEaT3KiwsLFvYPd8Po9EYlbLLDPDef3SZ2TMP55qz7+xwZkbAGGMghBBCCKc0uA5ACCGEECrIhBBCCC9QQSaEEEJ4gAoyIYQQwgNUkAkhhBAeoIJMCCGE8AAVZEIIIYQHqCATQgghPEAFmRBCCOEBKsiEEEIID1BBJoQQQniACjIhhBDCA1SQCSGEEB6ggkwIIYTwABVkQgghhAdqZ0EujcCxDSux4dBfKOE6S60gRuTv67Fm7QH4UYeSalYacQQ/uLvj4J9FXEepFag/+asWFuRiBGzfgZQBi+BsIESxkus8NV+x/3bsTh6A+QMMUSiiDiXVqPgBvLyS0X+hKwyFVECqjPqT12pdQVbEHcGP0T0xubsQSgMLGNa637CaKeJwzOsJ7KbaQqg0QDsj6lBSXRSI/30nontMg02BDI0sTLkOVMNRf/JdLft0lSDw19OoN2gkDGMSodG+HepxHamGkwT8gvNagzHcKAZJmhZoSx1KqovEH0fOasF1hBFi4rVg2Z52viqh/uS92lWQpUG4+pcpBjjL8aTEDLbNa9evV/2kCPnjHkwGDoA8qhgt7ZrXsh2G8Jk05Cr8TFzgJH8EkXlPfKDJdaKajfqT/2rV56syJxKxBrawLChGS5t2qM91oJpOmY3HsQawsSpAScvuaEsdSqqNEnmPY9CkuxUKRebobqHNdaAajvqzJqhVBbksIwv4sA3MWnWA6b+Kh7IkEbd/P42QQm6y1UhlGchhbfChWStYNn+lQ4sT4XfuMA4dOoqbTwpA07yI6pUhPUOB1m3MYd7xA7xWPpQlSPI9gnPBNJjL7+39WZz4Fy78th+/Hr+GJwU0mrlUiwpyCZIiEtC4ky2a6b++RBJ3A0f3rsOa1Yfgn6vgJl4NVJIYgcQmHWFj/EqHykLgOWEmLmo7YWSPZzgw5Sv8lkx9SlSsJAGRSU3QobsxXhvOklj4HtmDTavc8duDXNCeV05v6U9Z6BZMmXUO9fuORo/8n/HpVweQRJ3KmVpSkJXICQuAyMYJFoIyMADFMRGIK32+VKedC6Z9MRBtaslvWx2UOaF4KLJBH0sByhiA4mhExokBJWDQwQ7d27eEvkKCEpkCZWVcpyW1ijIHYQEidO1rBU0FA1CC2IhYlAKATns4f/Yl+n9Ig7nc3tGfDAawsrVDu5b6KCsthpwxOuPFoVoyzU4Dxl2dYazMQ2nofuzy1IKuxXB8Zsl1rppLw7gb+hkr8Uwcgl92eKCergWG/s8K0LHB59tsUBT2M+Yt8UMvj92Y3pZmhxAV0jBGV2djKJ+VIvzAduysp422w2agPde5aqp39We3L7C5WxHC98/G8vu9sHX3F2hDw5kztaQg/03DCI4zlsGR6xy1hgYM+36JRX1f/ZkSub7r8e2eUkzZewLDP1BALAP0aMIXUTENw76YvqTv+1ck5fKf/anMxZ3vZ2GfeCp2HR+NlsoSyKBPE2I5UifO+yiFkfA5ehdJ8gw8vHARIdl0UqayFClHsXieN0SNZfhztxs+HfYpDsbTOWtSTZRCPL76O/5MkiMj8CwuBWXRKdZKUyD1+AIsOFGExtI/sXfJJIz67Gck0HDmjIAxxrgOQQghhNR1deIbMiGEEMJ3Ki/IUqkUj8LDUFT0z43Lc3JyVL2ZaicSFUEs/udRR2lpqcjKzERBfj4S4uNfW1cikVR3PFJBUqn05f+VSiUehYchP/8Zh4n4KSM9HenpaS9fl5aKUVxczGEi1cjJzn75f7G4BE+iogAAj8LDIJfLXy6TSqVQKumkOJ/J5XIoFP9cqyUWl+BxZCSHiSpP5QU5NzcHI4cORlhoCADglPcJTBz78Ws7eU0U4O+PqRPHv/xw+tFrJ3779Rdcv+aDFcuWAAAKCwuxaP48XLpwnsuopBxWLF2MQwf2gzEGuVyOkUMH4/atW1zH4p2D+/dh/969AIDU1BRM+GQMQkOCOU5VNQqFAp9NnYTz584AAKIeP8bn0yajrKwMI4cOxrO8PADAA7/7GOLiDKmUDrD5LDs7CyOHDkbEo3AAwNOYGHw6eSLHqSpHbaes8/Ly8Pm0KXBb8B2EwgJoaWmpa1PVonHjxggJDoZLv77wPn7sjeW+t27CpX9fnD7pzUE6UlFisRjrVrtj3MejkJSYyHUc3jt65De49u+HR2FhaNy4MddxqkRTUxNFRUX47ps5+HbOLBSLXv/GX1CQjwXz5mLSuLFvnP0i/PQ4MgKjhg3B2lUrUVpacw+gVD6pKy0tFY497aCtrf3ytKChoRGePctT5WY4Z2FphYEurmjVujX2/LiLPtRrmKHDR+DK5UsAgPra2pBJpfDY4YWx48ZznIxf1q9Zhb/u/YmY6Giuo6hUSzNzpKWmAACMTUwAxuD3MATtWrVEkyZNIBQKOU5IKsvE1BQymQyhEVFcR6kwtX1DXrRkKdq1t1BX85wRCAT48utZ6Nqt28ufmZo2x8xZszlMRSpLX18fm7Zs4zoGr9n16InpM76AQCDgOorKdbOxwXL3VRBo/PNRuGmbJ1qamXGYilSWVYeOWL5yFTQENXS+MlOx1NQU1qqFCbt75zaTyWRst9cO5tDDVtWbqXaBAf5sgFMfFhIcxBhjbKnbQrb5+43sxLGjbOK4sYwxxm5cv8a6dLBkRw7/ymVUUg7Tp01hgwc6s5SUZCaRSFirFibs9ElvrmPxzrrV7mz1yhWMMcYeBgawfo69WXhYKMepqm5gv75s/769rKysjD0MDGA9bD5icrmctWphwjIzMlhxcTFbMG8ua9XChJWUFHMdl7xDclIS+7Blc7ZutTuTyWQsNCSY2XTuxHWsSlH5nbr09PQwdtx4mJiYQEtLC3PmzsO48TXzD+yvsrCwxGWf69DR0QEAdLe1g76+PgyNjODUrx8AYKCLK06fv4CszEwuo5JyGDJ8OIYNHwk9PT3I5XKMHTcerVq35joW73Tp2g3s71nGtnY9cPWGb42foAkAR71PwdjYGABgZNQMw0eMhIaGBsaOGw9dPT3o6+vDY4cXets7QCaVQk9P/z0tEq4IBAL89PMBDB4yFABgYGCI4SNHcZyqcujGIIQQQggPqO1e1oVCIc6cPqWu5glRuT5OTmhfC+c9qMIp7xMQiURcxyCkXHR0dDB56jSuY1SY2r4hx8fFYYCTI1xcB6mjeUJURiaT4e6d2zTL+h1af2AKQ0Mj2HTvznUUQt7pSVQU0tJSkZSexXWUClNrQR7i4oyniSnqaJ4QlZFKpbBs0woAauQgrg597Xti05ZtsHfsw3UUQt6p9QemAGrmWFbb3PABTo6QyWTqap4QUo1SkpMxecI4rmMQUqup/XnIG9etUfcmOKNUKqFQKGr8XcjqOqmUDhzLqzaP5zK5HPVoLBMOqb0g37xxXd2b4IxQKIRcLkezZs24jkKqgC40KL/aOp4ZY8jMzISpqSk0NGroTSVIjaf2gnz7np+6N8GJpzHRcHV+fv3x/kO/ore9A8eJSFW8+LsTebfaOp49tm7Grh3bYWvXAx47vLiOQ6qgJo9lOhSsBJlMhu/mzsHgocMwc9YcuM3/DiUlJe9/IyGEdwID/PH74cO4dfcvBPj7w+fqFa4jkTqKCnIleG7dgpzsbGzctBkL3BZDT18fP2xYx3UsQkgFFQqFmPfNbKzZsBFt27XDVs/tWLFkMXJzc7mORuogKsgVFOD/APv2/IhNWz1gaGgEbW1tbPfaDe/jx/DXn39yHY8QUk6MMSxfuhg23W0xctRoAEBvewcMHzkKS90W0twCUu2oIFdAUVERFnw7F+MmTMTAV2540snaGvMWLMLihfPpbkaE1BCnvE8g0P8BNny/6bUnWS1ZvhyxT2Nw8sSbzz0nRJ2oIFfAGvcVAAD3NW+env569hyYmJrU6stCCKktEuLjsXrlCmz22I6mBgavLdPT08e27Tuxfs1qpKYkc5SQ1EVUkMvpj0sXcfb0KXjs9ELDhg3fWF6vXj147tyN82fP4u6d2xwkJISUh0wmw7dzZmH0mDFwHjDwP9fp0bMXxk+chAXzvoVCoajmhKSuooJcDlmZmVi2xA0zvvwKvXrbv3W9D9u0wfKV7li8cD4KCwurMSEhpLw8tmxGYaEQK1evfed6bkuXITc3Bwf27a2mZKSuo4L8HkqlEovmz4NxM2O4LVn23vWnfvY52re3wIa1q6shHSGkIu7fu4f9+/bAc+cu6Ou/+xnHurp68NjuBU+PrYh+8qSaEpK6jAryexz+5SAe+N3H9l27oaOr+971NTQ0sNVzB65dvQLfmzeqISEhpDzy859h/rxv8OXMWbDr0bNc7+luZ4dPP5+O+d/OgVQqVXNCUtdRQX6H2Kcx2LRxA+bOm4/OXT4q9/uat2iBtRu+xxK3hSgUCtWYkBBSHowxLFm4AE2aNMUCt8UVeu/CRYshlUqxw2ObmtIR8hwV5LeQyWSY981sWFhaYc638yr8/tFjxqK7rR1W/z0zmxDCnaNHfsNt31vY7rUb2traFXqvjq4utm33wv59exD0MFBNCQmhgvxWnlu3IC42Fp5euyr1NCeBQICNmzbj3t27uOZzVQ0JCSHlEfs0BuvXrML8RW7oZG1dqTZsunfHF199jfnffkO3ySVqQwX5PwT4P8Den3ZjyfKVaN/eotLtGBoaYdNWD6xY4ob8/GcqTEgIKQ+JRIK5s79GJ2trzJw1p0ptfbdwEbS1dWjCJlEbKsj/8uJuXL1622P6jC+q3J7LoEFwHuiC1Svp1DUh1W3z9xuQlJgEjx27UK9e1R5up6OjA48dO+F9/Bh8b91UUUJC/iFgarph64tHYCWlZ6mj+Srh4+O5+NhPdQmf91c+4Gv/0Fgm/8bXfbU86tw35MiICK4jEEJUQCaTcR3hP9GVFaTSmJq0amHCWrUwUVfzlZaSnMT27fmJZWZksJMnjrP4uDj2y8H9rLS0lG35YSMTCoVs6+YfmEgkYp7btjClUsnOnDrJFAoF27B2NVMoFGyHxzYml8vZxvVrGWOMXTh3ljHG2LrV7owxxrx2bGdKpfLl6+/Xr2NyuZytWrGcKRSKl69ftOu5bQsTiUTcdAhhjPF3f+ULvvaP57YtjLHnY0+pVLKtm75npWIxW7fanUmlUrblh41MLC5hVy5fYlKplP24ayfLzMhghw8dZAX5+Wy31w6WnZXFfG/dZMKCAnb29CkWGRHBLpw7y54+jWHex4+xJ1FRLDQkmF08f47du3uXXffxYYEB/uzK5UssLy+X3bt7l6WkJLN9P/3IsjIzmffxYxz3St3G1321POrcN2Qz81ZIS02FafPmkEgkaNO2LRITElG/fn0oFEro6emhpLgYurq6YIxBLBZDKpVCJpWiQYOGEIlEaN6iBWQyKQwNDJGZkQENDQ3k5z+Dmbk5kpOSYGFpiZzsbFhadcDjyEjYOzrC7/5fsOvRAw8DA+A6aDBuXL+Gj7p2w53bvhg0eCiu0UPRCakwW7seiI+Lg13PXgjwf4ABLq64eeM6nPo74+7t2xj18RicP3sWdj174rrPVYwYNRoXL5zHqDFjcefObYyfOBmnTp5Ab3sH/HH5ElwHD8E1nysYMmw4Av39MXLUaJw/ewYfde2G8LBQ9HZwgN/9e7C164EAf38YGhohISEeZmbmSEtLg4mpKd1AhFRanSvIAGBhaYmY6Cfo2Mka6elp6OfsjDu3fdG3Xz/cu3sHvewdEPDAD2PGjsO5M6fRt18/XLp4AUOHD4fPlcsYOnwE/P38MG7iRJw8cRxO/Z1x/uxZDBsxChfPn8OAgS4ICQ7CyNEf48L5s3Bw7IP79+5h4N8fFja2tggJeoi27dohJDgIHTp2RPSTKK67hZAax7FPX0Q9jsRAF1dc97mKrt1sEB4WCnsHR/jdvwcLSyvEREc/L5zxzwtneloaGjduDE0NDTRr1gzFomIIBALkZGdDW1sbEokEGhoaaNSoEbR1dKCrq4v8/GdoamCAwkIh9PX1IRKJ0MnaGhGPwtG0aVMkxMfD0soK0U+eoJN1Z6SlpXLdNaQmUtdXbz6fNhAKhSwm+glTKpUsPS2NKRQKFvTwIVMoFCw0JJhJJBIWHhbKGGMsOCiIMcZYaEjwa6/T09IYY4wFBQa+tvzF61eXK5XKl+97sTziUTiTSqUsNCSYyeVyFhIcxJRKpdp/d/Lf+Ly/8gGf+yctLZUxxl6O4eCg52PpxViLfhLFioqKWNTjx6xULGbhYaFMIpGwjPR0VlZWxlJSkll2djZLiI9nz57lsdjYp0woFDJhQQETiUQsJyeHJSYksOysLJaamsJSU1NYRno6Ky0tZY/Cw5hYXMKeREW98blCuMHnffV93jnLOjIiAmJx5S6CHz9mNADg5NnzlTtS+FvnLl2gq6tXpTZI3ZaTnQ0XZye0bv3hW9cJDwsFAHzUtdtb10lOTsKs2d9g5uyqXc/KJ7m5uUhMiH/vehUZz82aGePDNm2qnI3UPaEhwfh82pR3jtX3Kc9YLo+U5GQMcHHBtu07q9RORbzzwrxlixch4lE4mhkbV7jhF++Z8/VXlUsGIDcnB7fu/oW27dpVug1CZHIZCoVCfDJ+/FvXedeyF9yXL6t1pyLv+N6C24LvYGBoCE1NzbeuV97xnJuTgwmTJmPzNk+V5iR1Q3Fx8XvH6vtU5b2v8ty2FU9jYlTSVnm990r5YSNGYtGSpdWR5Q2u/Z042S6pnRz7Vm1/qs0Hht5nzlX5xhkA8PPePRCoIA+puz5o2bLKY1UVHvj5IS21eg/A6+SkLkIIIYRvqCATQgipucoycX//ciza4oOc0jicXjgSvhKuQ1VOFc5RlSA19CEiHwfg2uUkdF+/C9PaP29O8ewR/jh6HhHy5ujStytKj6/H7/pzcXK9C3RUFJyQqlIWPMLVS8kwsKqH9JhcaJrbw8EsE/7+iZA07gAHZzt8oMt1SkLIW8lT4LNxOQ4GZaLA6EMUaQ2AZWtdZHKdq5KqUJAF0GpghOZa+UjOFKKD7PlkbUncaWxwv4iG0zfAzdUc9SFH+H1tyLPKVBSZENWQFUTC99gepNkugPtEPRxbOgMHW47F0u964/FmN6xM+wkHZnbE26c61W5vHLCY9Ya9eTYC/BMgaWSB3s69YEYXQBDOiBC6zx1H5BPwVb9fsTXylUXKfMTeD0FyaQO069UL5spEhAZFI0+uCS1NAI0s0LtHa/DteLsKp6z1YNreGp0sTaH3YhZHWQLObt2L5F7zMad3A5QUy197B8uPxoNb1+EbEI/sxIe443MVN27chO/1GwhOFlc+CiGVoGPWAa0baaG9w2BYd+iFLmYaaGE3FL2tusCqtQ6KC4RQcB2SQ7KCKNw+vgXbL4hh2U0PD7d9gRmbg9DUpiOE55ZixS8RkL+/GULUQhZ5BLtvm2H6fFcY/euomYkT4XNgP+7laUO34Co2fLEUV8TmMFP649A2b8QK9Hl5oK3SvyErsh/gQYwUkqgzOHD0GHbNHYspi48j6e8vxyWJV3HwwG0khv+M+cv/gMTMHGV+e+F5Jg7Q11JlFELKTyAABJrQ1BBAoPHPkFDLY9BqEB2zjmjTRAsWjkPR+e8DFlO7IbC36gxLcx0UC4V1vo8IV4pwz/sPyGx6omlKOOLz5FBKshATEoEcGeA9fxluGU3CzE+6QHn/Iu5r2GP0oE7oOHAs+holIia5SqeH1UalBVlZWAgRTOA4cxW++/obrFj1MRoEHMHdLIay2KNYtOImjCeMh35YADR6f4wBnTph4Cf9YZgQjXQBH49XSG0mi3+Ep0VypIQFITstDJFZcuRGhCClKBpR8SUoio1AHJ24eeWABRDQPFDCC9roOGE5Zjs1hVRcCrlCCSjLIC2VQM4Ap0Wr4Jr3M9YeeARlw4aoV5iJdJESyqIUpAr1YdRMj5d7skoPEjSbt0ZLnUJkZYigtDEEAAg0GkCvPiAwcsaC+SLs2uSJcLN6EGVloFjZGSwlFYV6hjDQ5WP3kNqsvtVn2OXz2cvXa88Mefn/Wb/dwywuQvGILD4M0QVyFIQ9RLZ1MSKzypD3OAwpRaWIThCjWBCJp+I+sKa/I5Nqp43m1g5ojudzHWK9ZWClRShtUB+liQUokHbA2EGtcXHvRhx0W4g5A71xZeNaBEojEdqgF9ys+Dm9uAoFWYGsh+fwx4WHeKbIQeDpw2g+fBCmz+2LTb+7Y1eRA5jfNTDXMTBLPQJ/UT5kHcdhoPk57M9sj66CC/hh3X3IIkPQsNcyWGqr7pcihFRdfatP4eXz6cvXrx6wzDz8J2ZyEYqQf9Fo2gWf7bqOl4fW3a8//7fHT/CZCChzg3BVZxa2LLSEDgrgs3QCPPc5ovcqJ9TnKvRbVKEga8LU7hPMsPsEM177uTv2DypGXk4RBKMnwFCvHoBpLwev7U++cA6+jMiGruhvoQNlwWWsnLgVBxztsawPVWVCCCGqI8uOQeC5AASFW8BYkYVEaR98OtWGd8UYUNfftes1gFGLBm9ZKENOjD8uBATikYUJFNkJkDv9D6O7UTEmhBCiWjrWU7B29xSuY5QLBxPNdNBp8vfYMbn6t0wIIYTw1XsL8h+XLqJJkybVkeUNcjld5UhUZ+aM/1Xp/fFxcbB3cFRRGn45sG+vSh4ucfz3I5gwiY62SeWlp6VVeayqwtOYaHT5qGu1bvOdI3DYiBGw7twZGu94LJs6TZoyFY0aN+Zk26T2MDQ0xP5Dh1XSVkszM5W0wxdt27XHpClTnxdjQdWf0zRpylT0sndQQTJSF3Xo2FFlY1UVGjVuVK3bEzDG6Np+QgghhGN08S8hhBDCA1SQCSGEEB6ggkwIIYTwABVkQgghhAeoIBNCCCE8QAWZEEII4QEqyIQQQggPUEEmhBBCeIAKMiGEEMIDVJAJIYQQHqCCTAghhPAAFWRCCCGEB6ggE0IIITxABZkQQgjhASrIhBBCCA/8H07XRQAy91FRAAAAAElFTkSuQmCC)
physics-General
physics-
A particle starts from the point (0m, 8m) and moves with uniform velocity of
m/s After 5 seconds, the angular velocity of the particle about the origin will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAADQCAYAAABhhn+9AAAWvElEQVR4nO3deXhMZxvH8e8ska0SSyQqCJKIvZbaxVZqLy8S0SipnZbad7WrquqmTWyvrd5aammQltZW1E5VEUVr3xIiIcskM3PeP0IkFaGVOTNJ7s91ua7JOWfmuWXym+c55zlzjkZRFAUhhEVprV2AEHmBBE0IFUjQhFCBBE0IFUjQhFCBBE0IFUjQhFCBBE0IFdh00KY3LUv5MiXx8fKi4dgdxANg4sKSbtT2LYWvV0nqjd6Bwcp1CvEsNh20dwbWx86QjFHzKm8PbowzADq83xpNgJeRFFN+ajashb2V6xTiWWw6aC5Vq1JaDyj3iLlrfrzCHE9CkgL2Vahdy8lq9QnxvGw6aDpPX0rn14DxEmdOxaUtN107wq9XTOh9qlG1oE3/F4QAbDxo2NehaYNCaIjnYMQP3DYDmLm7/wCRRi1uVV6ljN7aRQrxbLYdNG0hXu8VgLdeIW7XIpYeTwDzDbZu3k+C9mWatqmNg7VrFOI5aGz/azL32DupA70XRWIq1pjglvD90l3ce2Us4Rvfw096NJED5ICgAeZojq5ZQviB/Wzf8AtX8SZk5VYmN3jJ2pUJ8Vxse+j4iNaNGkED6FAyhViTPWXfnsVQCZnIQWx84GUk8YEBJfkKO8PGMTnsOM7NZzBvrD+u1i5NiH/ApoN27ssOtJ15JPXMD/uXqdt3AR+Oak3JfNauTIh/xqb30ZKvHeanXy6QaOdG2br+VPaQc0BEzmTTQRMit8gZB0OEyOEkaEKowKaDtmTxIs6cPmXtMoR4YTYbtLi4OD7/5GMWzg/DYJBvnImczWaD9tUXnxMTE8PmTeEcP3bU2uUI8UJsMmjXr11jyeKFACQbDCwMCyU+Pt7KVQnx79lk0ObMnpVhuLhzx3b2/LzbihUJ8WJsLminT51iw7pvMywzm80smh9K7L17VqpKiBdjc0GbOW0Kmc2hHzl8mC2bN1mhIiFenE0F7efdu9i75+enrl+yeBFRUbdVrEiI7GEzQTObzXwwfWqW25z74yyrVq7MtMcTwpbZTNDWf7uWM6dPP3O7/61cwdUrl1WoSIjsYxNBS0pKYs7sWc+17Y3r11myeLH0aiJHsYmz9xVFeeLsj3LepdIeR164mGGd2WzGyUmu5yhyDpv44qdGo8HB4enXs8pqnRA5gU0MHYXI7SRoQqhAgiaECiRoQqhAgiaECmziqGNeZbxzip1bf+bMpVvEJII+vxul/KrToGkdvF6y/Geg+dpW5ry/gCPmxqxZMsji7eVl0qNZhYHIFX1oXqcZfUZ+yJrjcdhpo4net5gpAzrStKY/vefufnj3HAsx3yZixmjCftjPVVcfCzYkQHo064iN4PMPNvNXAhRpO5f1oR1x1wLmKN6Y2Jl+S8/y09y+mDx+YnFwCYt8Gt7b8SEfbr6JUqQNI0e3sEALIj3p0azAnGLC/PA3n2JnT/5H74K2CE2G9cffGVBiObDjEImWKCB+P/Omr+GK2RX/oRN542X5M7A06dGsQOvWmXl7a/PXzXgcivrimG6dOTmJJBOAFpdCBS3wBiVxInQSK86l4FxrMBOCS6HL9jbE30nQrERfoAS+Bf620HSNH2aFciAJtIUb0r+rC2uGteO/BzW0nj6TyieXsvHgX0TfN2BX2A//NwfRs4kz+piLrFv0NdtPXCI6EZw9/KjToSchrf1wztCAEePZxUxf8BsGhyr0m9SLsnqAB5zb9g0bd5/hRlwy+vzulChXm+btmlGuoMQwO9jEScWZKeVZNO3xxWs3rViJBZmj+TV8A/svxhBz9STnfz3KnqsFadCpBz36BlPmwBC6jtnEtWTQ6fVo3arTsXsAVVJ+JHTeNq6a3fDx1qK5F8MVh3oEhXTAN3odn87fS5TiRouPtxIa6Jm2f2C6tIxvxn3AxF3xePdZzXeT6+FsjmLHxADeWXaBgv596N+2EJHfLmLtoZvg3Z+VP02mltxU5IVJj2ZNioHY6Ciio+NINDvh5F6cQn+d5Jct6yhQojyje37J53+cITDsPCZ86b94LSOr2gPtKXSxHgM3RHP+vDtat9Z88l0o7d21YKpH/JEGzDwUze7v9/EgMBAXAPMNwqfP4bPd99CWDGbckHo4A8Y/ljP360gS8zXh/Xnv07UwENSJZp/OYM31kjjJ7lu2kKBZk86TRr3H0SjdoviTX9ArcCYbpnXl4Im5fFTeBQ2gdatBrfKP7qbjTKVK3ug2RGO0q4Jd5UY0dn+YCF0RihV1AFIwJSZgMANaM3e2zeKjH6KI0hTljbGjafxo2JqSghHAcICFY+bi+HYb/Gv40XT4PJqq81vIE+TzysY4V+5Jn9buaDFyfctc1l97OLLX6tJ9KmpwdHJAA6DNhzafA+lHd5rUNY/F7eOzGeu4rhSmULNRjGrrnvbG6ysEM7hbddzsEvkzYjZDAhpRs2JV2vaawurj0VhyKi8vkaBZQdLlfWxcuZLvf7ubyR+yA74+JVPfGNN1rt970V3oBI7Om8SqP0241BvCu+O7UDz9u64rQesZEezZt4XQGSPo3r4+pR2i+f2HUEZ37sLcY8kv2L4AGTpaQRxbJr3F8G0J6CtdZ9OWkZTP8C484NSZi5gAdCUpUUjD4X/YwuPjWwrJpxcw/b+nSXaszqBJPejm87ejiEnRXLmRgqtXDVqF1KBVCJijIxjZqjfrrv/B0RN3MVcvKp/IL0h+f6pzpkrtV3gJMEZuYe2he+l6tXjOrRnH7PAoFPLh1XE4bQul9ihK4gPiTI9fJTHx4aUfTPGY4u8T/+hFzLFE30lKfc6t0yyZ/BW/JuajXM8p9K6Yj4wHEI2c/epNmjSoRet+yzjz4OFLPIgmJlEBh0rUq+0mfyTZQA7vW4PpJrs/Hcv0//7IuYRCVGrcjGqF7hF17gS7jt3CqXxzOoX0p4NuPj1GRxBtBNDhUvk9loSPwnv7UNoM+IZrKY9e0IHSIUvYPMOfa/O70HnaPuIUAC1azGjL9GTplpk0cHmyFPOdPXw+aBhhP19BcatAjSoFuX30ABeMPnSctoiZgb7IDY1fnATNmpJjuHj6FH/evEeSSY/eqQCe3uXwK1nghcf05qhwhrbsz3e3X6bzwq3MbplVz2Qi7srvnDp7jZgkMzond3yqVce7oOxZZBcJWq5k4txnbWk1+wSF280j/KuOeMj4z6okaLlV/A3OXU6iYJnSuMnYz+pkbJBbOb+Mb3lrFyEekQGFECqQoOUgt2/dkrvp5FAStBxk756fCe4SyOpv/kdsbKy1yxH/gAQtB7G3t+ePs5GMHjGMvj1D2P7jNhITE6xdlngOErQc6uCB/fTt9TZDBw/i2NEjJCfLOYm2zCaDZjKZSEpO4e79BOISDMTHx1u7JJtkMpn4IWILwUGBTJ4wnvPnz2E2y/n2tshi82jp58GeR/q5spatWrFnz960nxs0aMCWzZvQ6x/PRvzT188L3IoUoeub3Qju3oOiReX3Y0tsskc7evRYhp/37t1LRESElarJOaKjovjis0/oGtCR/fv2PvsJQjU2OWGt02X8KoednR3VqlWzUjU5i49vWcZNfJ9adepauxSRjk2egrV9+w7+858OmMyppS1YMJ8ugYEZho550ZZN4bzTv2+m69zc3Bg+agwBXYLy/O/JFtnkO/Laa00p+JIjyUYTep2W4DfftHZJNsvBwZF+AwfSt/9AnJ2dn/0EYRU2GTRIvd2uvZ3Nlmd1Go2GwKCuDB85GncPD2uXI55B/pJzoCZNX2PM+An4lZOzhnMK1YK2fOkSmjR9jRIlS6rVZK7jWbw4K1etpb6/v7VLEf+QKkGLuXuX2R/M5PKli4wZP1F21v+lqtWqW7sE8S+pMo/2xWef8ODBfdauXs35P/5Qo0khbIrFg3bl8iVWLFsKQGzsPRbOD8NgMFi6WSFsisWD9tGsD0hJSbtcE5s2fcfxY0ct3awQNsWiQTv52wnCv9uYYVmywcD80K/kRGGRp1g0aDOnTc10+a4d29m9a6clmxbCplgsaDt3bGf/L/syXacoCgvnh3IvJsZSzQthUywSNLPZzKwZ07Lc5vjRo2wK35jlNkLkFhYJ2rdrVnM2MvKZ2y1ZvJhbt25ZogQhbEq2By0pMZG5c2Y/17Z/XjjPyhXLsMEvEAiRrbL9FA2dXk94xNYMy2pVq5L2+NDx3zKs02hST5AVIjfL9qDZ2dnh7u7+1PVZrRMit7LJSxkIkdtI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgQRNCBVI0IRQgSoXwU9/f2oh8iLp0YRQgQRNCBVI0IRQgQRNCBVI0IRQwfMddTTFcHZnBDuPneP63QekaBxwdS9NJf+WNHvVEwcLFylETvfMHi35rw2Mb1OH1j1nEH4ePCtUprRzNPuWTuLdDv60GbSK88lqlCpEzqVRsroed+IhZrULICzSEf+pm1nc04d8D1cZLy6jT9sx7IxxpuEHu1na3TNbx6GlPIumPZZ5OJHTZZmNpL3fsC7SAHZVadX+ccgA9KXeoEVVOyCRK39exWjZOoXI0bLuhIzJpAAYz3Lwl9uY06+6sIEtx1PArjRNW1TKEEIhREZZHgxx8A+kndd3rLh4g++Gtuf+b4Po91ZbfO6sZ+p7U9mbVIo20+bT13EtI9sv4JCmLVOmV+X35es4/FcU95PtKFS2EV3f6Usj55OsW/Q1209cIjoRnD38qNOhJyGt/XBW638rhJVkvY8GJJxazth3phJ+7gEKgFaPHhNO5bsy8bOpBJS9w9qBnRi/+SrJ6NDrtRSuFkC3zlVJ+WkeoT9exlzYlzK6i1xxqEdQSAd8o9fx6fy9RClutPh4K6GBT+7fyT6ayFWUZzIotw4uUAY39lZKFS+mlC7moXg9/OdXs5MyeX2kkmA4rEz3L6Z4FfNQvF+bofya9PCpsZuUwZWLKl7FPJTSVfsqG2+ZUpcbLyrzOxRPfY2Q1UpsJq16pWtHiJwu6300wznWD29Fs06T+aVwD+Zt/51DPy5lfHAtPOwg6dpelrzXhWEbEingqgG0FK5el3L2D5/vXJmK3joA7Co3orH7w+Z0RShWNHX2zZSYgMH8ZNNC5CZZBC2OPVNDGL3qFMmV32Ph8om0KVsQtwot6TN7IxGrh1HTRQOmm2ybt47rD8Oi06Xb7dM44eSQepNBbT6HDAdMNMjNB0Xe8fSg3f2e5d9eIAV7agf3pKpTxqcVrv0uA1p7oAVMN28RZ+lKhcjBnho0c3I88ckACslJBp4c3RmIi0tEAZxeqczL/7CDUtKOwSjIHaxFbvfUoGndWxDwelF0JHN48Qw2nk94vNJwgwNhQ5mzLRZNwfoMmdACh4ehTHwQhyltw0QSDamPTPH3iX+UVnMs0XeSAFBu3+CGzHaLXC7rw/sJZ1g3YwKfrNnPVWNBfKrVwMc1nksnjhEZbUfphsEMmfAWyXPeYMz30alnh+hcqDR4JetH+LBjeHMGrbqaOumNA6VDlrB5hj/X5neh87R9xCkAjvj0XsZPUxpmaFoO74vc5JnzaADmhNtcOHOWK9GxJBn1OLgWwat8JbwL2z/rqf+aBE3kJs8VNGuQoIncRL74KYQKJGhCqECCJoQKJGhCqECCJoQKJGhCqECCJoQKJGhCqECVu8nI5LPI66RHE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVCBBE0IFEjQhVJDtF1CNi4ujR3AQSUlJma5v1bxp2mNFUXi9RUuGjhiFRqPJ7lKEsBnZHjQXFxdq16lH2FfzMl1/5vTpx9u6utKqTVsJmcj1LDJ0HPDuIFwLFHjmdgFdgvAt62eJEoSwKRYJmqurK4PeG5rlNsU8PXm7Zy/0elUu/y+EVVnsYMhbPUIoXrxElus9s1gvRG5isaDZ29szYszYTNeVK1+BgC5Bsm8m8gyLHt5/o30HKlaq/MTyXn364OZWxJJNC2FTLBo0rVbL+InvZ1hWp249WrRqY8lmhbA5Fp+wrtfAn8ZNUufOdDodffsPwMXFxdLNCmFTVDkzZPS4CQC83qIldevXV6NJIWyKKkErX6ECnQO70Kf/ABwdndRoUogsbd4UTnR0lGrtqXau4wez51DllapqNSdElhaEfkm3oC6sXb2auLi4Z24/p3UVKnqXxNerOBVbzOJoMiSTxJHZrajm44WvV3Gq91rFLXPmz1ctaHZ2djI5LWyGTqcj8sxpRg57j3693mbXju0kJSY+dfsR69cx6fWiKEYTugKFST3KoKWAe0E0BhOFX5vJ6i+D8HhKojSKoiiW+I+8qFKeRdMeX7x204qViNzoP+1ac/zYsbSfdTo9LVu3pm//gVSoWBE7O7snn5R0hmW9A5myMxavNt0p53Gbsyu3cL/+FJYv6E15x6e3J0ETedLfg/aIs7MznToH8nbvPniVKoVW+7cuKvYQc7t344sjcShAvkqD+WbdOGq8lHV7Fgla+pAIkRN5eBQluHt3ugZ3o0gR98crEk4Q1iOID3+JQQGwL0PAZ6uZ1a4EuixeT4ImRBaavNaML8MW4OTkBMZLrHu3E6O3OdN17nBe1R1n0cgwThr9eCt0DVOauz/1oIccnRAiEwULFmLI8OG82a176v6aOYpdU0MYvzmKckMWMq5DNRxpS127WAL7/Y+vB4fgPH8poxpmHjaLBC079qlkH01Y0tP20ezt7endtx/93xlE/vz505bPC2zOF/tvYsCOmMjT3DBVw0sHWkXBpAEl7hhh3ZtzesIqlvcu/8TrysEQkSdlFrTOgV0YPnI0Lxcrlu3tydBR5Hn+DRsxdsL7VKhY0WJtSNBEnlW+QgXGTZyEf8NGFm9LpaFjElf2rmbl6gj2nbhAjNkOEo04Fq/Aq43foEu39lQtkjHzMnQUlnTwwH5erVkLnS6rg/LZx/KnYD34leUDm9MqaCz/O+tBx5nr2frzfnb8uILRzfUc+PJdOjVpx8SNFzBYvBghUtWuU1e1kIGlezTzDTYObMWwTTdxrD6Cr1eNoJpzhg249f1QAvqt5rLWm7eWbmFa49SrZ0mPJnITi/Zoxt+XEfb9TczaEnQYOeBvIUtt3qPFKPrUd4KUC6z5/BsumixZkRDWYcGgmbl58CAXjKBxrUmDmk+k7GEFRalbtxx6wHBiP4fvW64iIazFokG7ezf1fDBtIXfcnzoc1uFWuEBqIcZYYuKkSxO5jwWDpuEl59RvUysP4oh76p6gmfsP4jEDaB15yVm9HVQh1GLBoOnwrFKRIlow3/mN4+eNT9kugZO/ncME6Mu8QmVXy1UkhLVY9GCIfZ1gAio6gPE0a0MjuJ3J17yN51ey4qe7KBoX6nQLooJMoYtcyLLzaPmqMvDTKbQorufGxlH0n7GVq2mTZWZiji5maM9Z7I93xu/Nj5nVvXSW3+kRIqdS5cwQ853DrPzoQxZuOEC0S0Vq1/bD4eZxDhy9jN6vOUHvjmJA27Kkvz6WzKOJ3ETds/cNUVw4fY7rd+Mx5nOlaJmK+Hk6Z9qtStBEbqLuHpF9EbyrFcFb1UaFsD65h7UQKpCgCaECCZoQKpCgCaECm71miBC5ifRoQqhAgiaECiRoQqhAgiaECiRoQqhAgiaECiRoQqhAgiaECiRoQqhAgiaECiRoQqjg//L0j3Rix9a1AAAAAElFTkSuQmCC)
A particle starts from the point (0m, 8m) and moves with uniform velocity of
m/s After 5 seconds, the angular velocity of the particle about the origin will be
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a
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)
A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALUAAAB4CAYAAAC0JbPDAAAdOUlEQVR4nO2dd0BT19vHP2GoOAARRxkyHQxtqzLV1lkn7qo4UJwozjo6bW2rbW21WhcO3HXvibZOXCBuEByEISC4QIYyDLnvH1Z/tq8kAUKC8X7+hHPP+Sb55ubcc57zPBJBEARERHQIPW0LEBFRN6KpRXQO0dQiOodoahGdQzS1iM4hmlpE59BZU+eHTsfLug62lnWw95jKyZzX//uM8G+9cbCsg62lBZ7TT5CvLaEiakdnTf0CCUaVKyMk72b51gQK//mrPGUny7bHg4G+VtWJlA06bmpDPujTE3uDp1xYtZzwZwB5XF61nNMFjejYzgbR1rqHjpsaKjgPx7+lMfLEHSzbnoQsdRfLtsRj1iWQT211/uW/k+j+p6pXh56je2Gln83Z4KWsD1rOybxGDB7THmOJtsWJlAW6b2qgivdI/NwqUxi3jllr7lC9UyCDGhhoW5ZIGfFOmBp9B/qO6kYdPTlyA1cGje1E9Xfjlb+T6PDt6kXw4csYRJN245jcN5W/ao7Cz8kAKPhfSzFQUbcQdJGcUOG3Li6CvUVtoWEzH2H2X4+Fwv80kSVuFyZ41RVsLGoLdk4thNErr2tFqoj6kQiCeJsS0S3EmaWIziGaWkTnEE0tonOIphbROd6aJb0nGRlIpVJSkpNQ9mRbp04dHBwdqVHDHIlE3DZ81yiXps7MzCQiPIyw8+e4euUK0tg7ZGRkAFCxYkX09Ir+gREEgby8PACqVauGvYMjjT/4AC8vb9w9PTE3r6mR1yCiPcrNkt6TjAy2b9vKrh3biYm+AYB13bo41quPtXVdrKytsbSyxtjYWGlfT3NySElJJjk5meSku0hjY4mPkyIIAvYOjnTr0YMBAwdTq3btsn5ZIlpA66aOvH6N9WvXsHf3LiQSCc1bfkSjRu/ToGFDqqlgYFV59uwZt2/eJCrqOmdCQ8nLy6Vj5y4M8R+Gm7uHOE3RIbRi6sLCQo7+/Rcrly3lYkQEpqamtO/Qibbt2lOlatUyHz8vL4/Qkyc4HHKQhw8e4OLqysjRY+ji0w1DQ8MyH1+kbNGoqQVBYOf2bSxc8Dt3ExOpVasWnt7N6dGrj1bMVFhYyMUL4Rw6uJ84qZRatWszekwgQ/yHYWBQLh83RFRAY6ZOiI/ni2lTCDt/DltbO7xbtMTDy5vq1atr/adfEARuxsRwcP9erl29grOLK7/Om49ro0Za1SVSMsrc1DKZjBXLglgw7zeqVqvGIL+hvP/Bh1SoUKEshy0xN6IiWb92NWmpqQwfNZopU6dTychI27JEikGZmjoxIYHxgQFEXb9OF5/udOvRk0qVKpXVcGpDJpPx1+EQdu3YhoWlFYuWLhPv2m8RZWJqQRDYtmUTM2d8Q3UzM8YEjsfWzl7dw5Q5aWlpLF+6iIT4eKZM/5xRAWPR1xeP6pZ31G7qgoICvpw+lZ3bt/FJx0708x1YqqmGXC4nLTWV+Pg4EuLjSbqbQFpqGoIgf2P7mrVqUdfGFhtbO+zs7LG0siqVEQsLC9m3Zzd7du2g5Ucfs3RFMFWqVClxfyJlj1pNnZWVRcDIYVwIC2P02HF4enmXuJ8Tx44SFXmNhPh48vLy0NPTw8nZhabN3KhXv/4bjSoIAvFxUi5ejCDqeiQy2XMMDQ2xsbXFydmFtu0/oUYN8xJpir4RxR+/z8XO3oE1GzZSq1atEvUjUvaozdQP7t9n8IB+JCclMfGzqTg5uxS7j3spKRw+dIAzp0PR19en5cetcHNz54MmTWjUuDFGRpVV7is/P5/oG1FcvXKZSxcvcvL4MZ49e4anlzcdOnXB3sGh2PruJiYy77dfMDIyYuOW7dja2RW7D5GyRy2mzs7Opm+v7qSlpjHti6+wrlu3WNenpt5jz66dhJ07S+s2benRqzdt27encmX1/czn5+cTevIke3bvJOTgAT74sAk9e/cp9lz/0aNH/PbLbPT09Ni9/xA1a4qxJOWNUpu6oKAAf7+BXLl0ia++nYmNja3K12Y+ecLOHds4deI4n3TsxKTPptLQyak0clQiIT6ehQt+Z8+uXbi5e9DXd0CxphOPHj7kh5kzsLS0YuvO3eIcu5xRKlMLgsDUyRPZu3sX0774CmcXV5Wuk8lkHNy/jwP79lDXxoY5c3/nwyZNSyqjxNyMieGLaZ8RFRlJ+w4d6dWnr8pLjomJCcz+/js8PL0IXrte3IEsR+jPnDlzZkkvDl6xnOVBSwgIHE+Tps1UuiYtNZV5v80hPOwcn02bztz5C7G0siqphFJhXrMmffsPoIa5ORvWriHs3Dnq1W+AafXqSq81NTXF3sGRjRvWk5uby0cft9KAYhFVKPGd+kxoKIMH9KNVm7YMGzFKpWsir1/jj9/nUrNmLZauWEnj9z8oydBlQmzsHQJHj0QaG8uoMYF4eTdX6bod27ayd/dOFixaQo9evctYpYgqlOg4V9LdRAIDRlG7dh0GDPJT6ZrI69eYP/dXvLybc/Cvo+XK0ACOjvXYeyCE7j17EbR4IWfPnFbpuh69emPv4Mj0KZOJvH6tjFWKqEKJTD3z2xlkZWUyemygSnPQl4b+qFVrVqxei4mJSUmGLXMqGRnx2+8L8B04iOVLF3P2dKjSawwMDBgzbgISiYTPp05BLn/zppCI5ii2qcPDznPs779o36EjjvXqK23/0tDNW7QkaEVwuQ1keomenh6zfp6D78BBLFu6mDMqGLtOnTr06NWH6BtR7NuzWwMqRRRRrDm1IAj06NqZhPh4fv19AZUrK94Mibx+nflz51C/QQO27dr7Vi19yeVyvvnyczb9uYHRY8fRouVHCtvLZDK+/nwaEj0Jx0PPUrFiRQ0pFfkvxbpTHzkcwrWrV/AdOEipobOzswlaspAaNcxZve7Pt8rQ8L87dv8BA1m9cjlpaWkK2xsYGDB4qD8pycls+nO9hlSKvAmVTS0IAkGLF+FYrz7eLVoqbb9180YKZTJWr/+T2nXqlEqkttDT0+PHn37B2cWF9WtWKc2O6tqoMU2aNWPFsiCeP3+uIZUi/0VlU0dcCOfa1Sv0HzBI6UmVmOhozoSeYumKYJxdih8DUp4wNDRk0dLlSGNjOXf2jNL2/X0HcT8tjYMH9mtAncibUNnUK4KW0szdgwYNGypsV1BQwPo1qxgzbjytWrcptcDyQF0bG2bM/J7Nf24gJydHYdv3LCxo0649K4KWiHmvtYRKpk6Ij+f4saP06dtPaduD+/eip6/HuAmTSi2uPNHPdwCO9RzZunmj0rY9evVBGislPOy8BpRpn/zM+6TcTSAhPpFHuUUsaRY+5VFKIonxCaSk55WpHpVMvXHDOlwbNcLSUvF2dkpKMnt37+anX357K45tFQc9PT1+/nUup0+dfJVspyhMTExw9/Rkw9o1GlKnReQPubp7FqPaetKqhQctBy5HWvifNoVJbB3hjpu7Bx9/3I2JS0+WqSSlps7NfcbWzZvw8FK8bSyXy1m7Khh3Dw9afKR4+ettpX6DhvTo2Zu1q4OVPgh6eTfncMghHty/ryF1WkKvJh6+n/KB6Qsr5UasJjj031O03IjlLDv2GAHQq/UJ46d1LFtJyhrs37uXvLw83Nw9FLY7d/YMN2OimTRlqtrElUfGTZxE6r17hBw8oLCds4srxsbGbPpzg4aUaR+JUWWMhCT2BW0m8VV54WR2L9lGAgYaK8Sq1NSH/gmoN1KSJuDcmVAaNX4fD08vtYkrj9jZ2/NJx06cUxIboq+vT5Nmbhw6+O6sghg2+ZTu9gY8DQsm+PxTAPIuBbMqtACXzu2pqyFXKzS1TCbjQliY0qNZubm5xERH071nL7WKK6/4dOtOSkoy9+8r3pBxdnHl9q1bpKc/1pAyLWPowpARH2EsT2TP0u0ky1LZu3QzCTW6EtDPVmPJ0BWOcyMqkmfPnio1dVTkdWQyGV26+qhVXHmlTbt2VKxYkSuXLils19DJGYAL4eGakFUO0KNO7zF0t9Yn+8wKlq9dQvDxPFz8AmmrwfLCCk0ddu4cxiYmWFhaKuwk5sYNnF1cec/CQq3iyiuVK1fBq3kLYmIUr4IYGxtjXdeG82fPakhZOaCKN/5D3TEqjGPj96uRmnUmwK+BxubToMKd2sHBUekOYmzsHZq6ualVWHmnaTM3pHfuKN1gcXB05EZUpIZUlQf0se8fQNf39JDLDXAePI5PzDRbhUXhaHfu3FG6Np2fn09iQjwffthErcLKO02bNSMzM5MHDxQv2VlZWSONvaMhVdpCeFGy5H/lhQmY0p+W7QOYMtTp3+UqBEFpeZPSUqSp5XI58XFSpVOPxIR45HK5Vg7OapP3P/gQiURCfFycwnYWllZkZGSQkZ6uIWWa5inn/pjDkftyCi4sYOSsv8iQ6+Pg+zsb1n5FazM9KEzk4OqDJBeC/MEBZgWuLFNFRR6BTktNJS8vDwsld+r4uDhMTU3fucQuVapUoaGTEwnxcQozUVn9c6g4TiqlqZmZpuRpkCp4Tz/EpekKmujb0HNJOD2XaEZRkXfqlJRkAExMTRV2EBcnpUkzN63nmNYGzdzcSUxIUNjm5cn0pOQkTUgSQYGp0//5uVTm1Yz0dKyti5eRSVewtq6rdA365Zf9SYauTj/+Tcihg7h/2BjXBo40e9+VkEMHNa6hSFMX50N4F+/SgPJv/Gu8LJmny8RJpYwLGMXDhw/Jycnh0aNHjB8bQJxUqlEdRZr6XfgQNElGuu6/nyGHDiCRSP61zCkvLORwiGbv1kWa+tmzZ5rUUSKysrJ4/PiRtmWoRG5u+X8/S8ubluwFQUAu1+xhiSJNbWKi+AGxPBC0eBGtmnuRnZ2tbSlKKa+5TtRJh06d/l/eE4lEQpt27TSqo0hTm5Xz5afHjx+xbs0qOnXxoVq1atqWo5Tq5fz9VAf16tVn4ZKgV0Vdq1SpwsIlQTiXIFd5aShynVqVJInw4kTI8+cFahOkKsuWLqGgoIAJkydrfOyXPH9eoHLpjerVdd/UAF27dadDp87cvnULBwcHrVQ2K9LUNWrUAKCwUHEaLUsrK25ERalXlRIePnzIhrVr6ec7ACsra42O/ToxN25gYaF4x7Ww8EW0vNk/7+e7gKGhIS6uqqV1LguKnH7Y2L7YIXygJGbYzt6BqMhI8vPz1atMAUGLFyKXF2r9cO/FiIhX71NR3P8nCY7dO7bjqk0UPCiaYFajBvdSUhR2YGdnj0z2nKhIzUSi3U9LY+OG9fgOHKzVUNe01FTS0lKxsVVcOSE5OQmJRKLU/CLqQ2GUnqNjPaWmfs/CgooVK3H1ymW1CiuKxYv+AImEwPETNDJeUVy6GAG8+FIrIiU5GSsra507XV+eUVjTwbFePS5fvKiwAz09PWzt7LhyWfEpEEXkpV7hzJlrJD7Ox9DMiobuH9PMtur/+8bdS0lh66aNDB4ylFq1a5d4PHVw+dJFataq9epJvyiS7ibi4OioIVUioORO3aRpM6TSWAoKFK9u2NnbE3EhvEQZiQqTNjHNN4D5IUkYmlcl68JSAls3odPk7cTJ/t128cIF6OsbMGbc+GKPo27Cw8KUVvYSBIHbt27StNm7dYBC2yg0tYeXF8+fP1ca5O7k7ML9tLQSTUH0rQew6GQ4B1dMpK1rQ9x7BNKnsYxbO+eyPuJ/X6akpLts27IZv6H+mJtrt8xbcnISUZHXla6/3ruXQmZmJp7eJSuSKlIyFJra2rouFpaWSjMSuTZqTCUjIw7s21t8BYVpnF44ki5NmtB9/G9sConggdwAifwp2Vn/W05ctGA+FStWJGBsYPHHUDOHDrzI+dFMSS6UmOhoKlasWO5Kgeg6Sg+PNW/RUmktkwoVKtCkSVP27t5VzKW9QmJXjiFgTgj5Pddz7O8tLJj9BT1dqvJ6/FtiQgI7t2/Df/gIre/MCYLArh3badDQCVMlseZR16/RpJmblhKw55F29Qg7161gxYo17DgURmLOu1G6Q6mpP+3Xn9g7d5TmuOjUxYf09HS2bdlcjOFlJEvjycWQuk5OmADkxXE1Jp3X3/4/5s+jcuXKjBw9phh9lw3Hj/7NzZhofLr3UNjuaU4O165e4VMVkmqqn0KSNk9i0Ni5HEkyxLxaFhHLRtLerQ1Td0iRKe/grUZpeQxBEPikzce4NmpMrz59FXa26c8NXLl8kVNnw1S+O+VFr2HS6FkczbChVet6PL16ltjsAh4/fEpNrylM/6Y703xaMmHSZ1pPaSYIAj6dOlC1WjUCx09U2Pb4saPs3rGd8MtXtVoqQ5aVjDQ2mcf3jzFv/CKu1hrBxpOz8CzfpXdKhdI7tUQiYYj/cM6fO6t0daNXn08plMlYtXK5ygIqOfuz7MQljm/6hZEDh/P1xrOEXb1NXEoK4Ts+I3TlXKpWq8bwUaNV7rOs2Lt7F3HSWAaqUGYv7NxZ+g8cqDVDF6adYvHodni4dWTS3A2EXLyP3FCCPCeLbB2fhaiUkKFHr95kZ2UToSTTUKVKlejdtz8L5s3lbmKi6ioMTKnb2B0PT3dc65q8Snxy5/Yt9u3dw6iAsVqPxHuSkcH3387Ap3tPpcFet2/f4tbNGAb5DdGQuv9QeIdVgcOYe7iA7mvPErJpCT9O74Nz1XfjhJJKpq5atSoD/fzYsW0LMpniGZmXd3Osrevy5fSppa4pOH/eXExNq+M/fESp+lEHP836AX0DfT7p2ElhO0EQ2LppI527+mgv2EqWRFxCLhjY0LDhizjuvLgrxKTr+C36H1ROneM/bAQPHtznxLGjijvU02PAYD/OnjnNymVBJRZ2MyaGQwf2EzA2UOuVvcLDzrNty2b6+Q5UWgcy4kI4t2/dZPSYsa/+JpPJ6Ne7J5de253NzMxkzk+zXkXxqZWK3gwZ3wk7/RP81NePSWP60Kl/MEkV9BCehLIqSHntmjchCAJz5/zMw4cPXv0tTiqlX++eZD55oi71pUZlU79nYUH3nr3Ys2uH0qNe9Rs0pItPN+b8PJtLERElEjZ/7q+Ym5vj5+9fouvVRX5+Pp9PnYKnd3OlaYqfP3/Oti2b8PTyplHj91/9XRAEwsPOk/nkxTnF40f/pn3rj9i/b6/K8djFoxJOQ1fx94WzbPhpDL7DvmN96FUiYu6RcPcqWya3KFGvEomEE8eP0b71x+zbsxtBEHj6NIfwsPMUlKNqZMVKcjZm3Hiys7PZuX2b0rZ9+vbHxtaWgFHDlWYxArh96yaZmZkAREVGcuRwCAGB4zEyUlyvsSwpKChg2meTyMnJZuiwEUpPzR8+dJD7aWlMmPTmgwsZGRmMGTWCYUMG8+D+fQwMFIbelBoDUxsauXnh4dYIaxP1fHkMDSvwJCODCYFjGDLQl9R7qWrpV50Uq+ItwBfTprB18yZ+/HkONjaKwy4znzzhl59mUZCfz+btOxUG9qxauYI/fp/L8JGjuXTpIjdjogk9F6616LaM9HRGjfBHGhvLl19/S5333lPY/vHjR0z/bDKe3t6s3/jvtfrnz59Tz9YaM7MaOperumrVquTk5BBxNZKaNbUbvvCSYqejnDxlGhUqVGDdqmClD4ImpqZ88fUMKhlVwrdvb9JSi/5WGxkZkZWVxfx5v3Em9BQuLq4aPXjwOllZWfTr05P4uDi+mvGdUkMDbNqwnoKCfL78ekaRbb6Z+T1du3VXp1St0qp1GxYsWqxtGf+PYv/+1a5Th1FjxrJowXyOhByiU5euCtubmJjw+VczmPPTj/j7DWLHnn1vfPB7vSy0XC7nxPFjtPR0Y9AQf6ZO/xw9Pc2kg5XJZIwdPYL09HS+/PpblUJcw8+f40J4GH369sPJ2bnIdqYmJiwOWk7vT/sy48svMDA04OSZt6ssXY+unUlJTmLmj7Pp3NWHqMjr2pb0/yiRU8ZPnEwzN3e2bd1MUtJdpe2NjY2Z/uU3ZGdlMWKo3xsrVhm9oda5mVkNnJycy2aF4A1kZmYycdxYYqKjVTb048ePWB28EgcHR777YdYb20gkEtzcPTAxfbG+3bpNW/4+eYphI0apVb8m+LRff46FnqWLTzckEglVqlTFzd2DCoaG2pb2imLPqV/y8OFDunZoTyWjSnz3w2wMVXhRmU+esOiP+SQn3eXzL79moN+QV0//p0NPMdj3RZyERCKhZ6/eTPxsqtLjUupAEAT27NrJDzO/pVo1YyZOnqKSoeVyOb/M/pHkpLvsO3QEO3vF8dUimqHEv+k1a9Zkxeo13Lt3j7Wrg1U6IGBiaspXM76ji093Zn47g+5dOr0621j5n1UOC0tLfp03n9lzftWIoeOkUnw/7c3kCePw9PJm5o+zVT5Vs33LZm7GRLN42QrR0OUI/ZkzZ84s6cV16ryHvb09QUsWIZfLcXZRfixeIpHQoGFD3D09uXUzhvlzfyU7OwsLC0vy8vP4dd58WrT8CEPDso24efbsKUsWLmR84BiqVKnCuAmT+bhVa5XXjf8+cpjt27bw/azZ70xVsreFEk8/Xmfl8mXM/mEmQ4YNp137DsW6NvpGFFs2/cn9tDT8h49g9NhxGCs591cacnOfsWHdOpYtWUyFihXo5zuQpsXMr33xwgX+mD+X0WMC+fKbolc7RLSDWkwtCAI/fDeDNauCGTzEX2l8xH8pLCzkSMghdu3YhkQioXXbdnTp6kObdu2oXLn0W+T5+fmcPnWSgwf289fhEHJz8+ji040evXor3fb+L2Hnz7F86WI6d+nKgsVLNbYqI6I6ajE1/PPQ9NMsVgQtpYtPN/r2H1DsD/zRw4ecPHGcC+HnSb13D319fRo6OdOkaVM+bNKUJk2bYWNrq/CuKggC9+6lcPniRa5cvsSVy5eIiozk+fPn1DA3x93Dk49bt1FaoOlNHD50kI0b1tH707788ts8lR6ORTSP2kz9krWrg5k54xu8vJszbOToEu0ICoJAclISt27GEB8fR0J8PMlJd5HL5VSvXp169Ru8ce4rCAJxUumrilmWllbY2NlhZ2dPvfoNsHdwKFGCeJlMxtbNGzl86CDjJkxkyvQv3t1E828Bajc1vCiRMHl8ICampgSMHYdjvfql7rOgoIC7iQnEx8WRmnqvyNWWWrVqY+/gQF0bW6X11FUhJSWZZUsWcTcxkR9m/6y9GGkRlSkTU8OLk9Qj/P24l5JCtx496dGrT5kH8KgTuVzO30cOs3XzRqpWrUbQymCFVbhEyg9lZmp4cVpk3NgAzoSe4j0LC4b4D8fFtVFZDac24qRS1q1ZRZw0FtdGjVmxao3SepIi5YcyNTW8WNn4c/1aFvw+j4z0dNw9PPEd5Ie5uXlZDlsisrOy2L51CyeOH6VylSqMGTuOkaMDtJJjWaTklLmpX5Kdnc3yoCUEL19GYWEhHTp2pmv3Hlo/1QIvlvyOhBziwL49FBQUMMhvKBMmT6ZGjfL3xRNRjsZM/ZIHDx6wdlUwG9atAcCne09atWmrloe64lJQUMC5M6fZvWsHT58+pW8/X0YFBGBd10bjWkTUh8ZN/ZKcnBy2bdnMqhXLefjwIW7u7jRv+REuro3KdENDLpdz5/YtzpwOJSI8DCMjI/z8h+E3xF/lkiAi5RutmfolhYWFnDp5gg3r1nLi2FGMjY1p6OyCk7MLTs7OWFhYlmpNWBAEHjy4T0x0NDHRN7gZfYP09HQ8vLwYMnQY7Tt0FDdRdAytm/p1kpOT2L93D+fPnSMiPJzc3GdUrVoNK2trLCwtsbSyplbNWkgU3skFHj96RHJyEvdSUkhJTuLJkycv8v01bYaXd3M6+/hQTw1r5yLlk3Jl6teRyWTciIrk2pUrSKVSYu/cJjb2zqsaKoqoYW6Og6Mj9erVx8GxHq6NGvH+Bx9qNf2XiOYot6Yuivz8fDLS03n8+DEZ6elkZj6hmrExZmZmmJnVwMzMTFyCe8d560wtIqIMMW5SROcQTS2ic4imFtE5RFOL6ByiqUV0DtHUIjqHaGoRnUM0tYjOIZpaROcQTS2ic4imFtE5RFOL6ByiqUV0jv8DGifCbNk17xAAAAAASUVORK5CYII=)
physics-General
physics-
There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portion is M. What is the gravitational potential at centre ?
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)
There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portion is M. What is the gravitational potential at centre ?
![](data:image/png;base64,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)
physics-General
physics-
A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
![](data:image/png;base64,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)
A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAACZCAYAAACPFLCgAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABgNSURBVHhe7Z0HWBTX+odzc9Ob/lPsBSVBo1GxADbEAiKKPVYQsfeCUUBEUBSxF0BFY0djbyBY0FiiEqMgKkVAbHRUmksT8Pc/33HhujdRQVEzud/7POdZnJmds9l55zvfKTt5BwyjYFhgRtGwwIyiYYEZRcMCM4qGBWYUDQvMKBoWmFE0LDCjaFhgRtGwwIyiYYEZRcMCM4qGBWYUDQvMKBoWmFE0LDCjaF5J4IKCAuTm5CAjIwO3b93Cjeho3Lt3D9nZ2Xj06BEeP36sPpJhXg8vLXB8XCz8fHyw0M0VUydPwrDBVrC2tMCEcWMwZ7YzftnqjSshl5Gbm6t+B8OUPaUWODcnF5eDgrB08UJY9O2Dtq1boHnTxtBv0gj6jRvCoKkuWjfXQ/fOnTDVZhL27t6NuNhYjsbMa6FUAlPKcCEwENNsJqOlflO0M2yJCWNHYf68ufBwXw6PFcuweIEbpkyaAHNTEzRtWB8dO7SF+7KlSEiIV5+FYcqOEgucJ1KB4KBLQs6JMuKam3WEq8tsHDtyGMHBQQgPCxMlVKYNJ08cx2pPDwy1skTjH75HZ1Nj7Nm9E2mpqeqzPZ/8/HyZU0dFRsr8mmGeRYkFDg8NhfPMGWih1xRdzTph4/p1uB4ejqTEJCQmJiIhPv5JSUhAclIS7ty+hRPHA2Q0NmlnhFHDh0qxS5JK5ObmiBvjCFa6u2PXju0yZUlLS1PvZZj/UCKBSSgS1kjku51NjOHl6YmrV64gJSVFlHvy9Z66PP33bSHx8YAA2P40BW1aGMgbICUlWX3WZ5OXlyfFHdi3Nzp1aIfxo0di365duH3zpozODFPECwUuFHnvzZgbQkIbkdP+AAfbaQi7FioibyKShaRJItrS0FnqgwdIFSnC/fv3kZKcjGRRSGbav22LN1rpNxOR2xS/iihcEg7u34cuIvWoVvEr1KlVA316dBMpyyxxQxzFmdOn4LVqJdzmuoicez4Wibx7zqwnIx90g4Reuyo7mfPmzMbihfM1yoJ5rnAV248fO4p0EdV/Fa0EHbdA5PG0n/YtX7IYEeFh4rMnwnvzJnluqkPjXOo6N21Yj0TR6kRevw6P5UtlWlVcj0yxjsh6Tv56XNTjIvsLRfUsW7IIYaJlS0lOwtYtm59Rz3y5nQIItXDRUZGinmXyu5D1uFE9s3D08GHZSp0+dRLzxPdSVM/ThbbTa0hwsLhO97B75/Yndc4XdYp66PN6rfSUaWBGRibuiWOSxWf7c3lybem7pvPk5OSor9qb54UCU+7725nTGDNiOMw7dcTmjeuLxaRCwqanp+Phw4dQqR7KnJVEpv/I+Lg4IXeKvIj9evcQubMubKdMltKEhV57ZgkWKcOyxYvQsb0RtKpWQoXyn6N6xa/RqH5dWFsOgJUotapXwUfvvoNyH3+Azz96H++8845MVa5dvYJt3lvwdblP8a7YVv6TDzXKR/9+B/8S23+aPBG3RES3mzpFHkfbaT/tq/hleewWLUDI5WC0bdVCnpvqePo85T5+UmcLvSYIunQRB/btFTfb13Ib7f9YnI/+njR+rKgnBtNtp+Lf4t8fis9cVE+F//sc27dtFa1ZCNq3afWMej6Q2w1Ev+PiH7/D9+AB1Kj0jdz2dbnP8NUXn+Kjf1E943BT1DPTwV6jnqcLbS//yQdYv8ZL3qA0UkTn+ezD92Q974u/a4vv1X7aT9jxyzasX/cz1q5ZjZ81ipfc5rXKU3ba6QaOEKnk2+KFAudkZ8uO2tjRIzDIoj/2is4YSVt0F9Jdr1KpZJqRl5eL7OwsZGZmyv03Y2JkLnz65K+wmTheDrM1qldHjl507mj8zGJm0l6Ocnz/bS3UrFIRVb75EpW+LCdf69SuCR0RkenCffrBv+UF/0y80oUwNjJ8IrCIZl9+/rHc9oXY/3T5QFxs2k65OQlMLQv9m7bTfvr7m/JfyBQm5HIQ2rRsLrdRHU+f5/MPn9RJN+Wli39g/949qCo+H22j/R+q65k4dowUmKQgaUmSonpIwO3bvKXAbVu3fEY978nt+o0b4Y8LQuAD+1GtwldyG0lJ8tENOEHUQwI7TrfTqOfpQtu/+Og9rFMLTC0ineeT99+V3yO90vdK18i4rSE6GbeXHfCnr02XTibi+nSAkfhefqjzLYxaNcfeXTvVtrx5SiTwEX8/TBg/BiOGWcsLRU0HyUsiU8QtmnkrKMgXEudIoSk6U7N6/XoEzohmzcXZCa0M9PCFOnK9qFBErCikrVG5goxsX37+Cb787BMhsBZ6d+8KR3s7OYlCTfV817lwdpwhm3tq4khiahZdnGfK/U8Xarpni+10U9LNR6kEHec6Z5bcT/uWLFwgWoInadJmEWHo3FTH0+ehJpq2r/95rRwivB4RLlOC2U5P6qS0hP4+4u8v6kkVHdpjmCO+A2rui+qhZpvSHer0btm04bn1rFu7BvHxcYiKvC5TnNlOjrDs3xffaVWHnggM9DkePLgvUpUTIi34Tz1PF9pOqRKNJlHLSFGWzu3mOkfuX+g2D2NHjUBd7Vpy9GjShHGYJepxsLctLo4iwtPrhLGj5WgUtZAr3VeobXnzlEjgo+JijxszUjbde/fsknkPCUy5L6UPWVlZcsaNJM7JycZDEYFJ4BgRgW+KKHfm1CkRgaaitRC4wfc6aN6ssWyan1Uo6jVpUA+1qlVGpa/Ko7poMuuLu72DiLDTbGxw5LC/zLn/16H0gyaNBg3sL4PEI9H5fVUoXTQVHee+vXvikkiNKCDEiD5QUbl166YsdOPRDUoTWB4rlqvf/eZ5ocAk5imRAowZMQzdzM1EZ2MT7gtxk5OedNQeCJEoClPUJZEpF6bIRh25ONHpINFpJMJyQD+ZL1JOeMjnoGwOn1XO/nZGdtAoYpO8JLyD/TQc8vWR6y1Uog4GcpiyZ9cusLIYgMN+h2R/5VWhfL5zRxNYiOgeLtIMVRa1ponF5UnrmywlpohN1/RvLXBBQYGcUKBpYX2R71HTFRkRIXreiU/yYFGo00bSUm9bjkRIwUUnj0YqxB28c/svIqrqy9yJvuiSQE37tCk2mCyasVWeHjJPLCgsUO9liHNnz2K0CCz9fuwlU52yuLEpAlPu279PbwSJVINkpdy6qNDQKJWwsFA5gkHBxfPvnEIQlOOu9HBHM90G6CZ6rtTLj46KkjkwCUypRPEYsPhb5sfilYaXLoqISuO/BqKpoZ4/DQW9CLppaPLiRMAxmUPT6AbzZyhPnyW+W4rClE9niHTuVflHCkxQGtG/Ty+Zw44YOliO51Ln5emZuHj1TBz9m8S+cSNajiv2EKlHV7OOUvzCgkL1GZ9NYWGhTEt4Gvn50DAljYebdmgLmwnjZdB4Vf6xAlNKQL3WHl07y7yHeqE0uH761GmRK4VLaSmliIqKxvlz57Bn107Zg+7SsYMcNqMB9OjoKPXZmLIgW/Q5/A/5wqRdG/QTnS7qZL0q/1iBCcpzabZrYL8+Uspe3btiup0tvFavgp+frxyt2Lxxo8yTBw3sJ4+h3Nduqo3MYXlJZdlDowF9enaXEh897C/H4l+Ff7TABOW6NKZJ46n0H9nesBUMW+jLWbNOxu1g1KqFLJQ2TBo3RkTpn+WXXBY9ZObPkGDTRAebhihpWOtVW7l/vMBF0Czbrp3b4TzDASOHDUHfXt3xY49uGDLIQs46rV+7Rg6JUTPHvD5omNPP10cufOos0jVK8/ILXn7B0/+MwJQO0JeXKTpaNGlByy2viDQh9u4dpKenyZELGk1gXj80db9GdOZo+nfK5Am4Jlo86gi/DP8zAjN/L2hIjRby0DAnrSqjEaGXgQVm3gq5eXm48HugSOEs5Rrq9evWypmz0sICM2+NLJUKWzdvQu9u5nJyY91aLzkTWppUjgVm3io0ueG5YrkcwqQlj7Tq7ayQkn7lUhJYYOatE3PzJpYsWSIX+LcQgo0aZo1tWzbJ4UzqdD8PSkNo3S+tr2CBmbdCYWEBEmLv4ufVK9GlUyc0qPc9Whk0w5SJ4+Czf598Tgf9DIiiMv3G8OlCSwZoOSVHYOat8TgnBSnXLsDHexMmT54OU7P+aNmiDdq1NoC5qbF8itJcIR8tBdi/by98DuyXxd/PV/6Uq0WzpnKN8eXgIBaYKQ0FKMjNQU5uIV44ilsgjhOdNlWOeI96k0QViZgLB/GL1zpsWe2B/esXwst1FsZPmglzy/Ho2KkLjNu0RBeRJgy2HIDxY0Zh4rgxstCSWasB/VFfRxtDrCwREhLMAjMl4REKs1Jw724EIq6E4MrVKNyIS0V67mNNOYnH2chLu4M74Zdw6fx5/BEUioi7qUijZSb5WXh0yQuHVjpi8mI/bPc/hMxAJ0RuGArHmYswbOkZ7D7yO3496oM1Ir2gnx3NoJ8K2dnKNS2O0+3lTGp9nW+FwBYsMPMihKAp1xDu54VN8+zh5DgLcxYthfsSF8yfPQsui7bAOyAS14uW+eYIsU+sFcfaYsaMuZjttgArXO0xy3EO3DYHwPdiFII3TcOG6cMxfn0I/CJjgCRP5AWMxRyHuRi7JAg3kuiWKJAPZ6Sfz58/dxbnfvsNZ0WhV3qiEuXL9AsaeuISC8z8NY/zUJgRhrC9znAdYAjj5h1gOtAOjotXYNVSe8y06gjz1sboYj0X8/3CcTVeiHPKHauHtYGJXht0tHaCywp3rHUdipHGTdGqvRX62a/FwikWWGI7Eo4Hb+HMgywRlQ8CIbMxd6oDrH/aj7Abz1/0TkLTL2e4E8c8n6w7SD2zEB7WTdCyUXO0tPbEooORuBkbh/jYGET5LoDXED20b9wYrYfNgK2XkHN0V/RppAt9c0fM2ROEmLh4JEQfhe/MHrDUqw/dJl3Qy6wlJkwdD5udUTgZmwRkbkX+OXvMnuYEa8cjCL2Zqf4Af01g4HkWmHkxeQm/I3hZNwxp+BlqNuiB3h7XRMRU7yTSzyJszY+waFwZWj/oo2mPXjBqoA3d+mbo7HgSAXeK1lY/ROaxWXDvpYOG1bXQqLU+zMdOwQCH7Vi/bROC94/DmUV9Mc1hMex+icaNe8+f0OCJDKZEqKID4D/FAN1rvofazS0x1DsGFzSCYySSjjvA1qQe6lapgurf10H1qlXR0GQsxmy9g5D76sMghIzyhp+DEdrVqY6aBmYwHj0PUx1WYovnIvh4TsbWOTbw2OKPA9GP8OCR+m3PgAVmSkR2zEkcn94aP2q/ixqNu6P38ssIiFPvlEQi4ZQzpnf6AfW/Lo/K9IitClrQ6zMTTicyEJ2tPgz5Ilofw3nPH9GzvhYqavdAP9ttOHsuCAk3IxBx9QpCr0YgJiEVqULeF60UZoGZEpGfGo7oHWNhb1wBtavooH6PuXDaeRWhcUlIjg1F+GkvbJ4hxG6shW8rlkeVqhVQqUIdGA5yw+ILWbhdHEmFkgUiHdk6HINFilHpm84Y4rAf99NVcm+eyDRKs7ydBWZKxuN05N3yhd8iK1gZNkHz5t3Qx2Y5Vu47jCM+m7Fj/ghMMm8Ig9oVUK3a/6FqzQqoXKku2gxagKUXVbhTbCUNi11CyK4xGN5QG1W/bI9BU3ci7t7L/RKGBWZKSKEIjWlIu3UOgbtXwN1pKhymTcfsRZ5w99qI3WtdsPInM3TRrQntml/h23oiD66mg5YD5mLBuYe4VdwXEwIXBsoIbN2wNipXNIPl9AOIvVecY5QKFpgpPTnxiAs9j8Bjvjhy5CROXAhC8NFV2GHbEab160C3QV10NK2LejpaaGBuC7tDDxBZ3OEToTjjGAI9e6FnvZr4RscSQxaeRVzqyz0njQVmXpE8PMq4iosbJsLOuAH0m3SF5egxcJvZGeYGNaHVzBIDPcJxIUl9OEQyfH0TDv5kgNbfaaO6iSPs9txBsurlHmHAAjOvRsFtxB6di/l99dGmaSd0nbIZO8+fQ8gxZ8zuUQ91axjCcPQu7Al70kkD7iPZ1wELzGqg4Xf6MLT5BZuu5yLzT4soSgYLzJSCfORlpuDerVBcv3wWZw/vxp5VM+AyvBv6dusLS7sN2BCYiGSR5+Ynn8SZxQNh2bQeGhkMxDC37Th0+gzOH/HC6pFtYVavHgy62cNpXwQicko38vA0LDBTCnKQefcyrh7djF1erpg3eTBG9++NgcOnw+HnAByPykBakYkFaXh4dTv2OPeDlWkHmPWfiMkznbHAzgJDO7eHaQ8b/LT+As7HPXrxUsznwAIzpSAPqvgwRP7mg6P7d2H3jl3Yd+AIjp4LRWhCFoqShGLyUnA/+iwu+G/Hji3e2LxZpBdbNsB7237sPxmGa4k5yHoVewUsMFMKCpH/8AHSE+4gLjYRSen51CUrASKlEKlHcuxdxNEMWxk+tYsFZkrH48d4XFiIwkLxqt5UYui9LzfY8ExYYEbRsMCMomGBGUXDAjOKhgVmFA0LzCgaFphRNCwwo2hYYEbRsMCMomGBGUXDAjOK5rUK/LgQj1Qq5GTnyEVLZbGMgwVmNHhtAhckIyPcFz6rF2KJ527sDnqAxDJYRccCMxq8HoFF5I0PwIXlvWChWwXVdczRzekw/KOzkaM+4mVhgRkNXo/ACbh5dD6Wda8F/W/ex4cfaUHHaDzsd4Ui+KF8wMBLwwIzGpS5wI9FjE3yg49Lf/Rr+C06GDVE08Y60K6pD8NRG+H1RyqEwy8NC8xoUNYCP1bFIOngNDj3NIKhkQWmLXHGXMdeMNbRhnYjKwxdfgaX0//iSfQlhAVmNChbgfOguu0Hf1sT9G5uDJMJ3tgbQj9idcUs41poVKkOWgxehpVBDxFfst9S/QkWmNGgTAXOuYE7R2Zjhpk+2plNgZ1/KmJpe/qvuOBmin71KkBL3woWq6/i9+SXM5gFZjQoO4FFWnBjP066mKObrh5a9XfF4rMJCEtMQtLt4wjaOAQjW9VA5cotYGC9HlsvpeBlRtVYYEaDshM4FXePzsOKnjrQ/7Y+GplYYZSjK1xcXeDmMhVOY83RQ68mapTTQp0WYzF99zWE58tHFZYKFpjRoGwEzgNU53FyqQWsm4k812QIBtktgfuKpfBYvhTuy5Zi+aI5WDy+M/rqVoOOTluYOvtg5+0C5JZyeo4FZjQoE4ELU5B/ZQW8hjWHUeNO+NH1GPZGZiMrSyX/j/oqVRZUmclQXVqFrRP00LLO9/iumxtmHUrCvVI+E4sFZjQoC4ELMyNwy3sobAy/R5NW42B76Dauq/dpUPAHgjYMhrWuNmrrDIDFgt8QnFW6ITUWmNHglQXOTUBS4Bp4DaqPZp9+iqo/WGL4lksITM//r8U7ItRm/47f11nD6rtyqPCvqqjb2QFzD4fj5oOSd+dYYEaDVxY47Q9c3zMNU82bQLdSdegaDoDl0gD43cjRjKw0QxcfgNOrR2CYYV3o1tBCAyMrDHHzR2BUmvqgF8MCMxq8ssA58bgfeQan/fZh97YdOHDoOI4H3xFRNf+/1jyICJx5B/GhdOxeHNy1HXsOHsOxwBuIf1DyJT4sMKNBmXTi3iAsMKMBC8woGhaYUTQsMKNoWGBG0bDAjKJhgRlFwwIzioYFZhQNC8woGhaYUTQsMKNoWGBG0bDAjKJhgRlFwwIzioYFZhQNC8woGhaYUTQsMKNoWGBG0bDAjKJhgRlFwwIzioYFZhQNC8woGhaYUTQsMKNoWGBG0bDAjKJhgRlFwwIzioYFZhQNC8woGhaYUTQsMKNoWGBG0bDAjKJhgRlFwwIzioYFZhQNC8woGhaYUTQsMKNoigQe2K8PrlwJQWpqKu7evVNc4uJiZYmMjMS8OS5oodeEBWb+PhQJbNG/L0JDryEzMwPx8XHFJTExQZRE3Ii5gfmuc6XAHiuWq9/95mGBGQ3O/nZGCmzSvi22em/B8YBj8PU5WFz8D/nikO9B/LLNG0MGWaBRvTpY5eGufvebhwVmNAg8dw5dzUxRR1sLA/r+iFHDh2L4EKviMnKYNYZZD0Kfnt1Qv442dGrVwLo1Xup3v3lYYEaDoIsXYdm/H7RrVoOebkO0MtBDK/1m/ykGzdBSvyma6TZA7epV0LThD9i+1Vv97jcPC8xoQB21LRs3wtHBHrMcZ2C208y/LC7OTnBymI6F890QdOmi+t1vHhaY0aCgoAAqlQrpaWlIe06h/VQyMzKQl5enfvebhwVmFA0LzCgaFphRNCwwo2hYYEbRsMCMomGBGUXDAjOKhgVmFA0LzCgaFphRMMD/A5KV/LV01thxAAAAAElFTkSuQmCC)
physics-General
physics-
A non uniform rod OA of liner mass density
(
= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut
![](data:image/png;base64,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)
A non uniform rod OA of liner mass density
(
= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum:
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)
A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum:
![](data:image/png;base64,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)
physics-General
physics-
In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–
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)
In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–
![](data:image/png;base64,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)
physics-General
physics-
A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of
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)
A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAC8CAYAAAAQGc7zAAAgAElEQVR4nO2dV3dcR7pY9wmdE3IkIkmABAgwSRQp0pI4ozvXGvmuuzwPchg/ePkf+KfcWcvPfvCLvWbZcydoKJGS7tWMRpQIJhAkACLn3EB3o3Of4IcOCAQlhgZON1VbC2JqdFej9/mq6quv6kimaZoIBBYiW90AgUBIKLAcIaHAcoSEAssREgosR7W6AVYQi8UIh8OEQiFCoRDJZBKbzYbH4yEQCBAIBKioqEBVf5I/niPnJ/dTjsVizM7O8ujRIwYHBxkcHGRlZYXKykra29vp6emhr6+P/v5+GhoarG7uTwLpTc4TxuNxNjY2CAaDxGIxIpEIy8vLzM7OMjo6ytOnT5mamiIajeJyuWhsbKStrY0TJ07Q29vLyZMnaW5upr6+ntraWhRFsfotvZG8sRImEglmZmYYGBjg7t27zMzMsLy8zMrKCltbW8RiMQBUVcVutyNJEqZpkk6nURQFr9dLZ2cn165d47333uPq1avU1tZa/K7eTN6I7jiTybC8vMzi4iLhcJhIJMLGxgYrKyvMzc2xuLhIKBQiFotht9tpbGzE7/dTVVVFXV0dPp8PyEbO9fV1lpaWmJ6eZmhoiGQySTAYZG1tjXPnztHR0UFNTQ2SJFn8rt8c3ohIuLi4yJdffslnn33G6OgoKysrRKNRFEWhqamJ1tZWqqurqayspKqqivr6ejo6OmhpaaGqqgq3242qqiQSCdbW1hgaGuJ3v/sd33zzDevr66iqSmtrK5cuXeKTTz7h6tWrVFZWWv223xiKGglN0zz0CJFOpwmFQmxvbxMKhVhaWmJiYoK//OUv3Llzh+3tbZxOJ83NzbS0tHDixAk6Ozuprq6mqqqK2tpaamtrqa+vx+v1kkqlSCQSRKNRdF2nqqqKs2fPIkkSra2t3Lt3j4mJCRYXF/n6668xTZPZ2VnOnDlDZ2cnjY2NYhb9mhQ1Eh62hHkBRkZGGB8fZ2xsjJGRESYnJ1lZWcEwDE6dOsW7777LtWvXuHjxItXV1TgcDhRFQZZlHA4HsiyTSqXY2NjgyZMnTExMEAwGUVWV7u5uurq6aGtrI51O88033/DVV1/x9ddfMzY2RiqVoqmpiQ8++IAPP/yQjz76iPr6+kN7zz8FinoJS5LE+vo69+/fZ319vTDYfxUx89eGx+PB7XYXxmvz8/PMzMywsLDA2toamUwGr9fLO++8Q0tLC6dPny6kWNrb25953nQ6zdTUFE+ePGF4eJipqSlWVlYIhUKoqsrY2BidnZ10dHTg8/kIh8O0t7dTVVXF/Pw89+/fZ3V1lYGBAdLpNIFAgCtXrlBdXY3NZnvtn+FPkaL3IzMzM/zmN7/h+++/R5blgoQvK6Ku60iSRGNjI01NTQSDQSYnJwvdpmma+Hw+zp8/X5i99vf34/f7kWX5uUI8evSIL774ghs3bnD37l0ymQyqqmIYBgADAwOFP1dXV3Px4kWuXbvGr3/9ayorK/n888+5ceMGN2/e5IsvvsDj8ZDJZHj//fdFRHxFii6hLMuoqorNZtsj4as8T17evHQul4u6ujqampoIBALU1NTQ09PD+fPnOXPmDDU1Nc99vng8zuTkJLdu3eLmzZuMj4+TSCQwTZNMJvPM4yVJQlVVHj9+jKqqdHR00N/fz8mTJ4nFYqyurjI2Nsbg4CAej4fe3l4h4StSdAmrqqq4fv06ra2tryVhvjt2uVy4XC4SiQSZTIauri4uXLhAQ0MDPp+vMN77sa5wZGSEW7du8fvf/5579+5RX19PX18f8/PzbG1tAWCz2bDb7fh8PpqamrDZbIyOjvLpp58SDAZ57733uH79OhcvXiQWi+Hz+fjmm2+4ffs2v/rVr+jt7X35H5ig+BJWVlZy+fJluru7C3/3OhIqioKiKOi6DsCxY8fo7OzE6XQ+9/t2v140GmViYoLPPvuMGzdu8PjxYzRNY3NzE6fTSUdHB2fPni2kXCYmJlhbWyMUCuF0OqmqqiKTyTA2NkY6ncbn83H8+HFkWcbtdhGLxVhbWyMYDBYiqmEYYIJJ6We/JEkq9Fr7yWQyaJpWeFye/M/YZrMVZRWp6BIGAgEuXrxYGGO9LvsFlmX5B9/4/scPDw9z69Yt/vjHP/L999+jqiqBQIBwOMzi4iL9/f1cv36drq4ukskkv/3tb7l16xbT09N4PB4uXbpEZWUlt2/f5t69e7hcLk6ePAlkBc9H+7W1NWZmZrDZbEhIWQFLPAVrmiaSLON2u/F43DgczkK6yTRNIuEw4XAEyD5OAkzA0HVsNhvVNTV4PJ7Xbseh5AlLYZaoaRrT09N89dVX3Lx5k+3tbc6fP8/Zs2epq6vjr3/9KyMjI6ysrDA1NUVrayu1tbWcO3eOra0t/va3vxGJRNA0DZfLRVtbGy6Xi/n5edbX17E77MSiMTLpNMlEgrt3vicZj6EoCvnLoGQdlADTxDAMTECSoKKigncuX6H3TB+QjYKDDx/y8MF9TNPE4XAgyRKY2fF1oKKC9z+4TvepU6/dnKKnaEqFhYUFBgYGuHXrFt9++y0XLlzg448/5uOPP6aurg6n08nq6ipDQ0OsrKwgyzJXrlyhpaWFd955h5mZGcLhMOvr61RUVNDV1UVTUxN3795lZGQEAJuqZocLssTgg/tMT4xjmiblsgil6Vp2aBIMUlFRgd1u3yPh0KNB/vD7f8bQdVxuV+G9RaNRjrW0cuLEydKTsBSYm5tjfHyc1dVVpqenCYVCaJrG+vo6o6OjOJ1OfD4fT58+JZlMEo/HWVpa4ttvvyUYDOJyudjc3GR7exuA9fV1ZFkujA1DoVDhtXTD4HTPadrbWgn4/DjsdgzDwMhJWDqX5D6kbJQ2TYN4Ik44HGZjY4NoNFp4iKqqnO7tJRqLkkwkSKfTrK+vkU6n6a2ppav7FE3NzUVpzhsn4cjICDdv3iSTyaDnxi5ut5vl5WX+/Oc/8/nnnxfSPplMBkVRyGQy3L17l4cPHxYqapLJJLIss7W1RTgcLoxD0+l04bUCgQBnzpzhrbcuUldXj8ftxjBNzCKNhw8NKWuhJMuEcxfpxNjYnuVHh8PB3/3i7/k3773P2uoqC/NzDD16RDKZ4P0PrnPuwsWi9XxHLuHLpmzyXcBBs7eDaGpq4vTp0wwNDTExMcHm5iaKopBKpUgmk3seu3vWbRgGmqYVHrM7R2kYBpIkIctyIX9pmgYejxvTMNE0HZfThT9QgWHoGEZpd8c5B5FlGUM3cNgdB34mkiThcrmIRaOMj43xdHQEWVFQFLWoQ68jkTCdTpNMJkkmk4WVkJdBkiS8Xu8LzcT6+vqoq6tje3ubO3fuIEkS9fX1JJNJMpnMnhUcwzCIxWIkEonCbN7v9+N2u4G9F4wsy2iaRiwWwzRNvF4Pfp+PjY0NZmdmqamuxev1omla0TIDh0V+OVWWZdLpVOFCPIhUKsXdgTv8+dM/8XR0hKqqat7/4Dr9584VrT1Fl1DTNKLRKLFYjGg0ysLCAk+fPmV9fb0gIfx4RMxHH4/HUxg02+12qqurCxXQjY2NB35vbW0tly9fRlVVkslkocvdn/PKF7Gm02kMw8jl/ty4XC7sufFdIpFgaWmJgYEBJicnkCTwuD20t7bi83kJBoNMT0/T09ODqqq5SUmpR0IpFwklZEn6wbHrxsY6U1NTjD0dZXlpGUmSWVxcYGV5mZra2qJUEBVdwlQqxdLSEgsLC8zNzXH37l2++OIL5ufns4P2F4wSeQkbGho4duwYmUyGZDJJe3s7Fy5c4N133+Xtt9+mpqbmma5almXeeecdLl26tOfvd89a89FgP/koKcsymUyG9fV1BgYGmJ6e4cmTJ+i6gdPlpKGhHrfLxdLyChsbG2haBlVVMAwd0yztTYy7I2F+eLEfwzAIh0NMT00xNzvD6uoqyWSCdCbN7MwMI8NPONN/tijV5kWXcHt7mydPnnDnzh0ePHjA48ePWV1d3fMYp9O5K2pwoAx5CfMThUgkwvz8PEtLS8zNzTE8PMx3331HX18fvb29dHZ24nK5Ct//omPIg9hdrZOvuBkdGSnMHqPbUdbX16mpqeFY8zHqc0uI+ej+Oq99FOyWUMqv0e/7CHRdZ+jRIF99+QXT01OYhoFqs5FOpRh69AiP10ttXV1pSphMJpmfn+fx48cMDAwQiUSArHh1dXXU1NQUavx+KCrmxQwEAni9Xubm5gql9sPDwwwPD/PVV19x7do1PvroIwzDoK+v77XaHo/HGR8fZ3BwkNu3b/PgwQPGx8fZ3Nzc87hEMsnyyipOp4szfX10dXVRVVVVaHM5SSjLMkj5FZ6dxxiGwcz0NIMPHxIMBrHb7ciKgmmaLC8tMTUxUfhsX5eiS+jz+Th37hxOp5Pe3l7i8XghN1dZWYnP5yuU0/9QUjcfVex2OzabjXA4XNhHMjs7y+DgIJOTk9y+fZutrS3u37/P8ePH8fv9OJ1OKioq8Pl8qKq6p3vd2Nhgc3OzMD41cysHhmEUxrALCwssLS2xtbWFpmlUV1dTV1eHy+Uiur2NaRpUVASoq6ujo6OD1tZWXC4XRn6cW7IJwiz5UWAhCh7QXkVRONPXTzgcJp1OE1xfJ5FI4PcHeOvSJa7/7OccO9ZSlPYcSgHD1atXuXTpUuFDztf35auaX4fV1VWePHnCjRs3+PTTT5mZmeH27dvcuXMHn89XKPFqamqirq6u8Jr5ScrExARTU1NEIpFCzk+SJDQtu3qQSqWQZZlAIEBtbS0NDQ00NjbS3NyMzWZjfm6WSDhb3NDU1EhDYwNV1dXoup6ddEkSPzzUtx4pnyeUJCRZ5qCrRlVVLlx8i8amZqYmJ7l75w7xWBKH08EH13/GJ//xP6MoxYn4h1JP6HA4cDgcxX5qAOrr65FlGbvdTnt7OyMjI0xMTBQiVyqVYmVlhWAwiM1m2xMJNU0r7EPeXaWT33lXWVlJQ0MDTU1Nhf3GgUAAv99PbW0tqVSKRw8fMD09RSwWzdZNqjZsqi27AlHi+cE8Uq77lSU5OzuWJA4Mh2TXlB0OR7bHyH2v1+crmoBQpism+c1Kly9fZmJigqGhIYaHhwtlWPkjPqLRaGGCk8dut9PU1IRhGNjt9sLuu6amJjo6Ojhz5gzd3d2Fwtl8SklRFGKxGJlUklQqycL8PGauGzdNE1mSMEt8LJhnz5hQ2jU7PsDD/Pvb83c/kFd8FcpSwjz5imeXy0V7ezsbGxtsb2+TSCSIx+Mkk8ln0jKFwThZsdxuN16vtxANGxoaqKmpKdQr7i4bc9jtqDYbam7TlJT/EGUJyZSQSzw1UyBXk5V9DztjwoOG6AfFx2IXqpS1hJBd42xra6Otre3QXyuZSpJJp9FyY93smEoq1BSWS/VMYQOanE8nSc9Nsh9UmFvs91n2ElqJBIXIWo4S5tMzViMkfE3yXXw5SrhnF6RpWrbaKCR8HQoD+p2lvnJAksAwQJKenyc8SoSEr8q+D06SssUAZYEkIUkGO3l1a9stJCwCEmTDiyzvSlTnureS8nKnbaYkZf9cAu0TEhYJCemZkyZKeYwo5f5XCk0UEhaZVzny5CgwATOXeC4F8XYjJDwESlFE0zQxctXkpVZ0KyQsMrvls3rGXC5pIyHhIZAXcXeV9lHKkM8D5svUSl1EIeEhI+X2cEhHEhHzB3WQTcPk5Ct1EYWER4G0b+YsZWUpthb59JCZ3dmeO+Kj9Man+xESHjJ50SRZ2lM2Ze7512KxI2H2ZLByOBdMSHgkmBI7FTc5EQ9FD5NC8Wk5ISQ8MqRCOX1hnLhrCPe67M4Dllwi8EcQEh4J0p5fpV1jxGKM1sxct2uUmXx5hIRHjLT76zWLHkzIRT0JzHLrhHcQEh4lu7casCPiq85ezcLEI7sUV9pz4OcjJDxKdhc3sKtbzh3F+7KUSzL6xxASWs3u8eGLRsR8BNx3gsWRqbirnXp8k0g0RSJtIKlq9oIyNDDBUJyodgdutxOHXUbh4GgtJCwB8kt7Uq7GL7s3fb9SO1Np0+KDOCXFnv1NbJDQw9v84Ysx7k9GkBobcfhcOEKrSIZKrKKH6s5erl3t4XSHn0rgoNPMhYQlxI9HxOzYz8jW5luYiM61T0uiJ0NEgqusLm9i6BlsbhVlfZJkJMm8toC3M4jh86M5ezhXDdX2Z59NSFhCZIuz94uYW+Iz81Ux1s+CTT13ZHLgHJXn6/lV2y95fytCMrpNLLxKeLOe6bExjJsPmf9+gc+9zazpNdReraS6/tlYKCQsOXZvmtpVjm+aGMaug0UtnYzkX9uB4qmiEhWbqrAlK8joOAMZ0ukwNXzJ/PIaT8fmUdpChM77OKhDFhKWHGZuF9yudWbTxDT1wr9bjSTn+lRjlsjT23z16V8ZGFpmwdmOVNtIb5cTd9qJ6nLg82goaOiZ9HPHsULCEmZ/gWypZAIlRQY0mL3HzJ0b/MutB/x1TEc910hbix9HpZcKR5gKrwuvI4aau3nP8xASlig73W9pbZiSANVugLHFzHdfcefzL/lu9QSr7df4L//h3/GPH3XRUxMiMaKT/JOTaSOKIsmgqCjywRdReezW/omRr4o2zfypX/mEdAnsIZXy5xvqpKMhYltBQnGDqOnC6XXj90hI8SCx1WWCkRgbsRTR8Cbx0AZb8TQHneclImFJke1ys4HPKM1iGBN0XQHFS+OJkxzvaadpcp6FkT/zlz/FiczXU78+yPboPf5yf56hDdg2H+Osb2d0uZWTJytotYN711MKCUuInY1JB2/LzKdpAMsOMjIBQzMAD77Otzh+Kch7wSmcszpeOU50NYiypaNLtdT2XKTvpIeEq4PWDg8VLhld36m5yCMkLAF2ul/zhW+xYWWnbGqpbAvafka74yT/rXeFf9iMEErLpCQHNocbp9OOx2ZiV1V02Y3d7ae6thK/A5z7Gi8kLBHyAr7I+rHVWzl3Ui0uPA1ddDQcp8PYJrIeZTslgb8ed0Cl8sC38uy4Vkh4lDxHnB+6n8uPURobmRSQfXiq3DgNQFVRntukAw5pP8ymCfaxX5b90U96wcNhchXZu7tx61FQbArKjz/wGYSEFlK0ahiLJyuvi5DwKMmdFlfofqFoa8D557K+a355hIRHiJkvRCC3SlBMAXf9Wm4RUUh4JOzIls8D6mbx7vtkHvC7ckJIeBTsqQWUDn0lxDSNstp7LCQ8ArIzWQPDKNza8FBOYNhzFk32N0V/jcNASHjIFMpSDfNwjv74AfKToNJI4TwfIeEhsbsg1dB1y0ZrpS4gCAkPFdM0CzdoFDwfIWGR2d/9lUIkyp/cWqoICYvM7kKEUvnwdy/vZdtkdYv2IiQsIvsjYKmsXpTChfBDCAmLjJm/UWEp7Q0xs6s10q7UUIm0DBASvj6FbcC5gtRddxUrZZ65y6eFCAlfk3yC2MhtSrJ6H9KLYppm4XR/qzkiCfMD4+wN/eRc3Vy+uzqa2ysUmcKiRDYCGoaBbpRHOmb3hMksgTs8HYGEJpg6pgmaLmfPWlFMwMDQ9exJA3LpbOx+GUzTRDd0dH3nqxwoSGiWxj1OjiYSSjKSaZK/231+/VQqnLdSfgIC2Whu7Poqke7tRymc8m9gGlkZpZ0PZg+Koj4zbpSVV6mffj5HIGHuzD1534tJErJSht1wgd0nZeW+jDKRUDpga4AkHViHeOCFVeSLTUxMXpHs52AWxrbZ86PLRML9Fw+wM8XKPSQ3e15dXSEejyNJEoqUHUNuhbZIJBK4XK6iNEdI+FLsjRT5D9DM/1cu3bG0q807ew72zE8MwyC4scHkxASh0BayLKHaZHRdZ2lxkYmJcdrbO/D5fK/dHCHhK1H4+LKpmTI8wLyw2f45EdwwDGZmphl88ID1tTVkWcFud6BpGmOjo9xraMTr8QgJLWHXGZVmYWJivNTpCVazJ0Wz6+iR3ZimyerKCpOT44RDISRJwmazoWkaszPTDD+po//cOTqK0B4h4auwK0eYPznLMAxLDzN/KXISGvDcO8HLskzzsWOcOtXD1OQkmclJUqkkfr+f2rp6Wtva8HpfPwqCkPDVyUVBIx8JcyKWA/lIKMPO/fD2jXcVRaH3TB82m50nTx7z4P59MpkMdrud3jNnuHL1KvUN9UVpT3ElNFMgOYr6lKXITtn8jnxGGUoIO8nq/QfBSpKEw+Ggvb2dru5uTnZ1MT83RyAQoPP4cbpPncbr9RalPUWWMPGTkDDLzilaul6+EprGD+/MczidtLd30Nd/FlmW8fn91NTWFU1AKLaEhvaTOfvVzN3R1TBNDNNAN4yyucumVDjnMDc7Np8dFRqGQWhri8XFBTKZDA0NjWxHIkiyRDC4wdzsLLV1dUXJFRZXwozx0xll5pe+jL1f5UDhHOxciuag+K3rOhMT4zx5/JhEPI7X66WhoZFkOsXczCwDjju8delt2traX7s9RVVmO6bhK04SvUTZWWWQZQlVVbHb7TgcDnRdL5/umNzERJGx2x0ospx7XzuPMQyDtbU1piYnME0TRVEwTBMJWF1dxW63033qVFHaU1QJ4ykozqS9VJEK9xfRDZ10OkUyEScei5WXhPnZsSyTiMfRNO2ZAlfTNNE1jUw6jWEY2B0OnE4nDoeDZDJBOp3CKFLpWlEldBUpb1SqyJKE2+1GkiTmZmdZWVlhfm6OysoqDLN8VkzyEpqGSSKZYGT4Sa4Mbaf9qqrSfeoULrcbTBM1dwdPgHQqhcvtpq6+BFM0nsAbLqGiUBGoIBCoIJPJsLy0xNbmJnb7AXcNLAMymQymaaJpGsdaWvB4dma8qqpy6nQPp073HHo7iiphtsqsBO61cUioqkpjczPvXL6C1+tlZWUZuXAfOuvYf/Nt0zRBkrCpKqrNBqaJbhjZIYOu7+wElEBVVGx2O1XV1Vy48JYl7ZfMculDBM/FNLOCHbTxvrCFIjfe2z/ug+wSnSwru+65fLQICd9gwqEQw8NPUFWVuvp6mpubUdWdu2yGQlvMz80RiURQZJnWtnaampuPvJ0/lazeG03+0KV8stxms2HoOgMDd/jy1k3sdgcnTp6kr7+fU6d7cDqd6LrO5MQE9+7eZWlxAVVV+fmHvxASljKldKLCfuZmZ/j+u+9YXFwguh0tDMlnpqeZnppElmVGR4a5f+8eHZ2dnDp9msbGJjbWN8hkMmQ0DSO3acsKhIQvSD6toWkahmGg5HZt5ScELzKqkWUZVVWLPpF5OjrK73/3/xh69IhgMCtW9nWyec38CbF2u4Oa2lrevXqVt96+BGQvLrvdjqwoKEXewPSiCAlfgu3tbb64eZOF+Tk6Oo/jdDqZnZlmeXmZ7e0IWiaDzW5HkmSM3FZQTdMKKw6nTvfwb3/5y6IsdeXXdqenp/j+u9s8eTzEzMw0iWQGjWymwmlXcLlchSPqwuEw0e1t/H4/qs1GIBBAUVQy6QxOp2JZpBcSvgTxWIx//ZcveXD/Ptd/9jPq6uoZejTI2NgYKyvLbEci5FNUUi51I0kSsqJgU1UikQiX371SFAlN0yQUCjE7M00oFMLt8dLc3FyI2JIkoek6uqYBO5HckVv1SCWTJOx2bDYbuq69dnteByHhS6AbBuFwmFgsit/v50xfHye7uggGgywuLDA9PcX42FPi8Ti1dXUcO9bC8eMnqKisxDRNmpubaWp8lYH/s7lXWZapqq7iTP9ZamrruPLuVVKpVLYM325D13QeDT7k/r17GIZOdXUNLa2ttLd30NLais/nZ2l5idmZGWLRKMlkAi2TKcrP6WUREr4EqqrS0NBAPB6n8/gJ+s+epaq6BoC1tTWejo7y3bd/IxwO0dbezumeXt56622cL1juZBo6pq6R0XQyGqAoqE47qiyhsFdDSZKoqKikoqKSrq7uA5+vrb0d1WZD1zSaj7XQ199PX/9ZKioqAHj8eIhMOg2mkS3GcFhTCyokfAl8Ph//+O9/RSQSobu7G58/UPi3mpoalJ4eKisrSKVS+Hx+qqqrX1hA0EmFZlgbuc+9hwt8PZTG032aK5/8nFPNHtoA248+x166T53G4XBgmiZer5eamtqCgAAtx1qwqTai0W0kSab52NGnZ0Akq0sInfj8HWb/5f/wv//vIP/0hxgV7/+C//pP/50Pz1bzFuC0uomHxE+kDvr1OfxrVcHlsNFcbdAQ0HFgIOlGbl/wm7oan0V0xy/IUaQvJLsDf6WdhmoHVT4DxWnDLkvZXXFvsIkiEpYg2T0fCopqx+lxYQcU/QcKZst8QCUiYalhZs+VlqQ06XiIzcU5Vjz1zMeCuBSFhOrB7nDhdjlwOVQcNhm5zCOkkLCkkAAZRU2hqissjHzNl/8jzmx7Bcd9GpmtGKtLSWzNfTRe+jlv97fxXrcXX4muab8oQsKSIl/zpyNJMRJhk6WxCexaNY5GheTCHLMPxgn7F1CDXuKGRFtTN8f9Kk7Kd8goJCwpcnuBNQVd81HZfpYLn/wnrlw4zuWqDK6Fb1k8+c/curfKn/7yB76z67T0tJHp8tLnALVMLRQSlhQ5CQ0FQ/fjb+ji1PVf8M7lAB8AnFahYpzNtW+48a93mX/SweBimpYG6K2hbEOhmB2XEvnDKlEwJReqzYnXDQ7IblB3e6G1naqGChptERyJCFtBg8h22dza+ECEhKVE4VAiCUyJ/J0PDCBb5yKDw4XqdOKwKdhlOfsBlrGAILrj0iI7OcYkjaFto6dSxFN2NMAOYGoQWiOxlWAtWYHpDFDXoFJZeeCZ52WDiISlhOoEfx2eSj8N/gT2xDLzw5NMjKaZ3wwTH59k6v4MMxsKWlMfdcePc6rJRrOfss4VikhYSriroPUtmrqXeff4A75d+Z5v/tf/ZONBC4l+MOZGGPl6kDk6qf37f+Dy9Uu812TnuC2/57s8ERKWEpIPfN3Udy/y7vvjZB5HSEU2MFYyrFTbSQYzrHIMb+d5Tn94lXfPt9MVUCn3M4fiDx0AAAFTSURBVKhEKVdJYQJp0tsbhFfmWVkOMr8aI66ZSE4nss2FzeHFX1NPTWMjtQEXNS6pXDMzBYSEJU0ac2uZzXCK9YQDe6CKmiYffqubVWSEhKWOnkLL6KR1Gclmx2GX37jZpJBQYDlv2kUlKEOEhALLERIKLEdIKLAcIaHAcoSEAssREgosR0gosBwhocByhIQCyxESCixHSCiwHCGhwHKEhALLERIKLEdIKLAcIaHAcoSEAssREgosR0gosBwhocByhIQCyxESCixHSCiwHCGhwHKEhALLERIKLEdIKLAcIaHAcoSEAssREgosR0gosBwhocByhIQCyxESCixHSCiwHCGhwHKEhALLERIKLEdIKLAcIaHAcoSEAssREgosR0gosBwhocByhIQCyxESCixHSCiwHCGhwHKEhALLERIKLEdIKLAcIaHAcoSEAssREgos5/8DSI7Ts0lRMMgAAAAASUVORK5CYII=)
physics-General
physics-
A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg-
and radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be:–
![](data:image/png;base64,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)
A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg-
and radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be:–
![](data:image/png;base64,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)
physics-General
physics-
In figure, the winch is mounted on an axle, and the 6-sided nut is welded to the winch. By turning the nut with a wrench, a person can rotate the winch. For instance, turning the nut clockwise lifts the block off the ground, because more and more rope gets wrapped around the winch. Three students agree that using a longer wrench makes it easier to turn the winch. But they disagree about why. All three students are talking about the case where the winch is used, over a 10 s time interval, to lift the block one metre off the ground.
Student 1 By using a longer wrench, the person decreases the average force he must exert on the wrench, in order to lift the block one metre in 10s.
Student 2 : Using a longer wrench reduces the work done by the person as he uses the winch to lift the block 1m in 10s.
Student 3 : Using a longer wrench reduces the power that the person must exert to lift the block 1m in 10s.Which of the following is true about student 2 and 3 :-
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)
In figure, the winch is mounted on an axle, and the 6-sided nut is welded to the winch. By turning the nut with a wrench, a person can rotate the winch. For instance, turning the nut clockwise lifts the block off the ground, because more and more rope gets wrapped around the winch. Three students agree that using a longer wrench makes it easier to turn the winch. But they disagree about why. All three students are talking about the case where the winch is used, over a 10 s time interval, to lift the block one metre off the ground.
Student 1 By using a longer wrench, the person decreases the average force he must exert on the wrench, in order to lift the block one metre in 10s.
Student 2 : Using a longer wrench reduces the work done by the person as he uses the winch to lift the block 1m in 10s.
Student 3 : Using a longer wrench reduces the power that the person must exert to lift the block 1m in 10s.Which of the following is true about student 2 and 3 :-
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TfVUlPrHvl5RelpN+IUpISsX/vbultVwL82tWrQgCU4YO335RZZewcGOTy3ddfSZuc2hy1MvJG17gVmN8lBdAjA/iqADgDCyhBpdr62HlcjvtxcJ921ysvvyTsqbPIyc6+AWzaWvwQKK2ppmdnZcLYQA+vvfxH/P65X0qPONV6lrzh+CjX/c3/+Z/wsVDx6XxjWxpnzwgbfLcMluAHw49j4+tR84Pwwvy8AFiVMIMOQ/PcWRmIUlVRIaXwSWEzMzJNlexsrOTQmL2tNTrb26UviMS4DDqbzpw8gT+9+Ac42tnK74NEQUQTa/d338g0UgqFS6mpsjPX1tSQjlnuS97oGrcCEwdzdzBbbqV7A/jqqlAJZkTDonGhIj9upprFF1UvgEvHGCt8+Pp4yWUmflASUP3u6uoQgK+Q9tw3X30u7Teqf3q62nJYhVVBKKmPHz6ED955Ey+/+LxMdsjKzJA9e2REuPwwDgmbkJ0Fs+j4MDe6JjXfP8/L6rytsDQ3xbHDBxEkzCRqVXExMdi54yu4ONqvfXEKamlpkp00nZ50ptLjTs0qLTkJB9ZGQii9aX4pnXA0yeh9P3/6pMwVp48kJkoxTCbNL/EdT01Nbnh9W4X5DKgN3QvdG8CF2kP7aUo0TGfb42ZqD+z9Q4ODBHC/kFFJdKoR4LUCmFTLWerH3dUZhxnP/MMeIRGOyDBFqmeU2jyWXlWGMb756p/x6Yfvy84iWah5JUJNrKhUVOfkmOobYnt2Zqa0xS9PT4lreDL3vd2Y4KI/gsOS+/Z8L2us0SHGd7dDvJdzApTcT5V6ursQ4OuDUyeOyvgGdtTsoNlx852qOtdIVPP3ChPA0txkLXqxWgKb/hoG2KyurkhvPkFy6/VtFZ4WvPCoAc7a6FR/HjdzOIDqyNWr14TNbYSXX/gDvNzdZX1oes0b6plj3SDVMAaz/PGF38PUyFDa3wxnZO62MsSPjriQoECZoMAACRch6RneSukvZ4yghiDswU8/+kCWBRroH5BSZ6PrUvP9Mztqfkd8L3S0EbDMp6cE1hLqM4NZ+B5vHRIjsSM/f/oUPvngPakB0MG2EcVGRwkwv4XAAD9pZlF6s1PgGDhTS6neX56+fNu1bTVemF9Yu+PN6Z4AzsnOWHiRGT2PmylFee4lYX8xy4jDWcmJibKGF8NN+YHQY84QVUruM6dOyFRBAprRTXLcfGhQBjZIoAsbLFT05H98/nfQF+11iHUEeA2H0cRH5O3lgUP798k4aK6ng5Eey42uTc33z8qYCkpgOjhDhBSmNz1B2N8EOP0gyrhyVaI/hPYzC27QCUpt4NYJ+OiAot1OM4tj3xymtBLS+7OPPxDtxyqEhehgNrqurcaLi4trd7053RPAr127Kos+zM7NPnamrUEmSHVEL8xyPJeELcZxbDrYaCtTRY8IC5N2HUFLhxuTCnjM1LRQ8WcuS68pgwQ4bMUO4o1X/gQjYd91tCsATju+WqhzEcIOZ07x0UP7UVJcKD2VPP9G16bm+2ShifHDnBO/C/JzcVS8L0YeFubnySwvOtree/tNVFeuj0nnO+CxHKqdEiBlmCZNtlsBTicqPfQMZ6XaTy87bXcOqbJQAtvhudnWhte3hXh5WRHVdze6R4BfE6rN4g2wPU7mB0EJ3t7Wioua56Vql54uAC7UaWaHMUSxqbFBvtwTRw/L4Reup21GB9n8gpD+4trZ6zECjmpbYny8TEChys9YZUoQdgpU01NTU6CroyXUxx3Iyc6S98/JFze6NjU/CM/Ld8qwUz8fb3wgbGNmiDH+nzb1999+I73iqlFtSoBzuJSdNOPJCXDlMBH/sjYbK7B+/smHyEhPl0EwcvnjD+X7pgZATZQSfOPr2lq8sqIYUbgb3TPA2WPQq/y4mTYTPwjW3qId9d03X0pv6kYAP3X8qIx+omOFEpwFAmbFC2U7fMH8MAhwFvmTADc1kmrfOoCnJENX+4J01OTn5sj75/lvvS41PygrAE7iu2PpYyaNyJiG4iIZt0Cpnp4mbHFhHpEIYAKaAO/p6ZIqOr8LJdGM8vZwxzdffA4LMxPk5mbDxFBfEQhlZSFtf9r11EI3vqatx7zne6F7Bjh7DErCx80878rqirTbGL/86Ufv41JamuzxCUiq6FSxqaLTBuf4OFVt2tzMKmKCA206em+5jiCPiYmSY+nsDFRVdNrgYaEhUhM4dewIqirK5f2zc9vo2tT84Mz3SuDW1VZLJ9gHb78lJTf9I8fF82ccOjtwJRGgtLGpyjOai9KYxL9U6dkhU8UPCw6WWWPvvfUXOcTG7CseS0BsdB1blTkacC90TwDni1A+pCfB18T5+SIZuiidbElJ0gZn6iErmjaI3wTmZ0Id+3bHV3Jcm9KBHnQOwxDYTEZQFoNwcXLEb375M5lj3NbapgLwGngICcKOws7G+kYCw5O89+3JyzeCVvhsG+rqZPbX63/6Dxw+uB9mwnSit9xQV/tGAAuJnTyLcUyorKOtfVzY8l9//inOnjop352U3BYWsmAHv11+O8rz3n4tW5OVHdzd6D4AzofED/1x882eikkFL/7+t3B3cZHDZJS4lOQEKMv+GOrr4WPxYezZ+Z2cz4rVQghw9uItzU2IigiXxfUZKMMhmlDR21MDoBee0oJqOotF8ONidhk9+LTyFABX86NlxYeqJHbSlLi0mZn2+7tf/VyWPqYkpy/kqngH1CTpYCOxTiCdpQf37sHzv/k1nvv5T2WRB46A+Hp7yk6dtF443XoNW5cfOcD5cJ8UK4lFAX7+k/9PqtDSk96gACYBzgnrWG6Xkpfj3LsFyFklhMEvvt5eMqiFxfg4Vn7u9CmZWkpAK6U3I+KkY+bQfmmfUzLw3AQ4H+at16Tmh2c+V9UPlY411k47cuiAlMJM/vnv//C3+Ej8trO2RGR4mJyMkAErNlaWePXlP+Lv//o/45f//hO5/8ULGjJAiSadkpTn2Oj8W53vhe4J4E8LEeD/+Hf/RcYVc/yUMecMTVUCtVWo4BznprPG1NhISPN38cYrL8vINX4MRw4ekJU2W5qapPpG51qtsNcZRMF8cRkE8/1OOUZL211NT4YYSqrU1n7105/IoKQXfvecfJfvvf0XvCTW//H53+Ol53+Hn/w//4KXX/g94mOjbzjv1HSTthjAbfG3osd+7hc/lap0Rkb6umQTxjXLogyCmTYaHhYi48qZJUabrECo8bTNaVvzr/ScCzueJZ9YCILjsty/VHQQqpJFTY+fWHyDoausp8Z0T6rdFzXOyXz9MyeOy0KNXG9ubCzNrTtFtj3rtKUAbmFmit/+8ucyFp3j1IYG+jcmiq8WQGdxe04KT7uaUWxMbOCwFyUzs5ZojzMSitKenQKPpbOuWACaEVDvvv2mTF5QOoDU9GTo6tVVGaTCdE++P5qIDFdmiCttdTpL52bnhF1+VdZXZy2+1paNU0qfddpSADcUUpuZRQSymVDBP/nwfdjb2MgiAnS20elGm5w2NR1njF5iDWyGqCqdadJbLsDNobSGxgZZ3on2HDPN6ICj7a2mJ0scAmLqKLU0pvLeqcNl8IuPpycO/rBHxkKo6XbaUgBnLDqdKcxLZy/O4n3MCqNtnsSssNISaZdT9VZlAlv+rlEsM6mE0psqPsdM6VT77KMPZBFANT15uhXgd7KtmSOgBvjmtOUAziEUjoPSi0i1m4Et7771F+khDw4OQnFRkZzogLW3KsorZOFFgpmpoCy6yG2U2vHxsbIeN8s1/fpn/y4DW9pab1bmVNOTIzXAHx1tOYBzojmGoJJom1H1ZuWOw/t/kNKcFTtZ78vH2wsJ8fGyUgsrrbI2Ngvk6+loY/eu7/DFZx/LzoH54f/9v/49/uOF38PJwU7Y6Tfra6vpyZAa4I+OtiTAWaVDlVaWV5CVni4TTViji1VbOCTGetss1XT4wH5ZYIBZRdzGtERGsdGrzmlufv2zf8Pf/fV/lnXBGOespidLaoA/OtoWAFfS8sqyVLOZeEIPLMMWmQv85Wef4MC+PdILHxsViXphh0vHzXVOc9MAPe0LeO7n/y4DYujBVdOTJTXAHx1tK4Ariel0jGFmYomcCaK3VxbDZ9IJ0xVVo4AYxlhfWyOTFZi2yJlb1PRkSQ3wR0fbEuD3S6xv5eXpLsdTGcKqpidLaoA/OnqmAX59eR6LLOawIqR4fYOs7MkgmpW7BroIDeAa0w9XsLJ6bzHBarp3UgP80dEzDfCrY83oaWtC1xXg8sI16VU/e/KkLA+9OV3B0ngDikta0Nq38cenpgcnNcAfHW1fgF9nxs11iP83ljmstlbkR2xbwUJjKsqyLyG7C5hZvI7k2Ag42lnLMsvziytr+wq6fhWrS4viQ1vGylWx9no/php8YGjkD//YFll+aGnl6s1zqemhSA3wR0fbE+DXlnB9jOGo9ajsWcDi7AT6S9JRVtOOPhaPnG5HeVEj2pKDUJ57CYk1M+ivK0VBgjtM9U5DS0MfrjHVaJ0kYq9gqjkVUU5mMDVyhH9mG/quDGCi1gEaJy7g5IGL8LSyhJ1XMgq6Z3Bv1arVtBmpAf7oaHsC/Pocrg8nIMg7BF7xdRjsz0Wszh5cNI9CamM7BipD4OCRhVRXW+QmR8Inox01IcZwsdCDlo0b7M1NcPGsNUJLmlHXkIdLTjowMjGDhbEm9G1DEZ5ehqFyB+gfPIL9+/TgKI4z0zgLk4gaVIz/OGKcHzOTZ1hEcrvTOoBHhMsaZCSpgQlWEgty+Hh6qAG+CW1TFX0ZWCpFmK0zHK3dUVztBKN9b+PD3a5w8Y5HTagBjIJLEetshBhvBxiHVyPf8QDOazvAOn8cI60FiD33A2wjfWHm7Arzo8YIqx3C+Ggp8lNTEB2fgf4iO2jvvwh9z2r0DpSjyf8oTlgkIqTi3mpl3Q9xKI8ztOhqa8mQW9WPfDsS75cAZwlsFnng0CZJWehAef8spujt6a4G+Ca0TQHOD2AS5T5uCNA+CJ8YbZw11cSOQ24wOGiCaEsdeBS3ozDGGpHudjAMqUKB81FYuMUgsFN0D30NKDTZB6cIUxw3dYXOcX9UTNCzfhXL83O4MtWMsSpnaGq6wyNhCNcXmzCcfBFnLOIQUnRvk8LdDzH1VfPsGRkzz6qhnIBuO9NNgF+UEwkya0y5nqys0MI66azCemDvbjXA70Db18kmQH452w8xZz/E8QuncDo4GnqGFjj17g6c13JEcvcIenNsEOZKgFej0OUE7HyTEdYrAN7bgBKLA3CJssAJY2foHPVB+WVK5iWMdHehoywHw+VOuKgXAL9kcS1LjRhO08M5yziEFc0oTv8IiSWE//TS8/iHv/lrcFoe1p/bznQD4DoXER4aghlhnpCUddyUIGfgEvML1AC/M21jgAsaiEG85sd4/81j0EuvRpzveZx85zV8qJOG8pErmM/Wh4+NGTT9ypFjvRcmztHw6wAWOiuRo7sT5iFBsPH1h/PxwzBw8YG/rxUs7fzgH5qE3iJrnD/vDpfoQWC+BgNxZ3BYPxL+eRtPVv8wxCIH2loaePXll2TFGarp25lUAR4WGiRnpiGxfDWZ1VFpp09MjguAu6gBvgltb4BfrUdFlBOMNf2Q3DaCnkp/hNgawjiuD/0zK7heG4z0OAHKzHbUxzogIqkImcPiQxppQ12wHSLy6lDSUInSQB3onD2Hc0eOQcchCrEVLRhrjYefbwqSiyaFBO/CRIkPXEMLkdX44/jRFTO7aMDN2VGG325nWgdw0clysj2WzqY3ncxJD5hLwCKNLKq5f+/3aoDfgbY3wLGKlcV5zM4sYPnqNVxbXcDi/Cxml8RvmukrC1gSH8zCkrDtFuewuLQMsQnXr4nlBbG8fBWrV0UbV8Yw0tWCtvZe9I/PYYFj3quc7WQJS8s8QCyvzGN+YRnLqz+OA4zF/p0d7OUzYFHJ7UwS4Alx0NPRkuW2OGUuy3bT2UamV51AHx0ZhauzE/bvUQP8TrTNAb59iB8265QxQ44prtuZbgBcWwA8MEAmDtH25rxiirnFFCAfGR6Rk1gwFbhRDfANSQ3wLUIcGmpuapST63G+re1MqgAPDvSTocO0vWdnr0jmDKHMGBweGhQAd9hSAL861IOhbsGPfjR1Q1IDfAvR6PAwPvnwPVmVZjuTEuCcBJIT+bMGH1Vy5dzYDPrh0BmLczg72mPf7l3rVfRrV7F8eRxjfS1obW5Ga/c4Zgioq1cwM9iGtrYudI0IE0yYX1cXJzDSI5ZbezE6NoyxkS60tbSjvW8SVzibz9wYhlvq0dzcgd7pJcwtLGJutAd9Xc1oaunGwMQcoy5USJhuk33obGxES3sX+oRJd+WKMBNHhXnXXoey6HCkZ+SgdGoWI6P96GPb4tx9k0vivsW+Iz3oaGxGe88IpoS9+LDFu9UA30LEcV9O1MekGE4OsF3pBsAvCoD7+8lZRamSc4ZYshLknFySddP5TFQl+LWFafRlhiDKwxgm5hawd49GRssQOmuzkO1tCDNTW9j4ZqKqrwOtdSkIsbGHu30IUmJ9EBFgCgMTJzgE5KJBdBAt5XEINjOArbUTPNLqUJSTh9Jwe7i5W8NCtOOfXIXGG6EP13F1vBq1SR5wMDURmpYZ3OKrkJVbh6pwO3g6WcDK1B7hlzKQ3VmJhAA3+JrpwdzaF4EJhWhtSUdioCNMNIzh7J+MokHRmay1/KCkBvgWIqqmFuLDOX3iOAry87bt5AxKgOsIgAf4+sopn2l7c14y8vT0tAQ65x9ztLOTJbhUAb462Ys694twdPOFb0oK8qMt5HCnznlLOBmaw9PdBQ5aF+GTFgaXsFDY63kgJb8MmV6GcDDUgH5AOmJjLqH+kgP8QwLgEJ6PksI4eNn7wfX0afg6msI+IRc5wabwCYhDYNV1JhALmkd7oh8i3dwQmpWJ3IALsPZKgLVjEi7ZacExNh1+jl5IjnGHX3EiLC9YITgiCamJsYi1OAsfH00cM3SEgbk/koWUL+hewPTdMpfvQmqAbyHih8+QVdaWMzEyxNI2naDhBsC1NOHn443BoQEpsVlNl8wAFwKdE1k42tkIgO9cp6Ivj3Wj0l4XvsllqF2ewGyDJfT0zuCtN8+JNr2RmpKAJB8nxBVEwt4vHA7mcWibuoyhmkvICHaBu38ovMysEG76PQx8Y+DTJbSC1V6kW5jD/NOPYePmgaBWcR0VLkLih8E+YxWKQl/jyHW0FZI6CtUr81iptYd/UDz0jaKRameMwLo+pAUGIyvUBPZ5iTDUC0VJ6wxW+gpQbrcfhl5uMBbnC3a1g7+3J3yyB9H/kGEVaoBvMZoYn8C5M6ex85sd6O/v35Zx6aoAZ528gYF+GezCcW8ypxGenJxAd3cX7G2tbwP4ykQvqp104OobiPCSTBTGm8DI1hIHvteE7nEdOLl5wdMjGNm1qQiMCIWNaSzaRiYw01uEgjBzGJ45gQOf7Iap3kHoe/nDNq4SZSUp8DF1gNXO/UI990B41yBGyh0R7BMCu0vLUPjMLqMh2gfBzm6Iys9AUbiWlOAmxnFItTFBcF0bEn29kRJgDIeCRBjrOCEmNgMlScGIttaFc1w8fIN84XzyKxzdfxCn/ZvR8pBT5KkBvgXJT3wknCI5MT5eqq7bjZQA1xYA9/HyRJ9QxamW872TWTabk0N2dnXC1sZKzibL6aiUtDrZjWq7Q9A5cwSHLprBwcoa3lnFiPYVqrHhaeiYWEBPyw6xxckIT0+Fn2cWusdG0Jfvj1BbDWjqWcBAwxQRyX7wCfGEqaY27G0MoOecJGxmD6SFCXu9bwSjdQFIiEqEX6ES4NcwVxuHFHddXBTXrnvgfRwyC4O5cw7yfV2R0NKN7KhI5MW7wq8gAvr7DkD3rNAqzNzgZOOOzHR3ODrbQ+/UKZibmsM2pQ/dG0hwduqqvBmpAb4FiVMda50/K/gcusVHvt3oJsA1ZM17Ru7RqTgyMix5dHREgHwUnZ3tsLW2lAUzVQG+Mt6LKnstOLu7w6esHU1tfRiZXcDMxDCG22pQV1uHuoYuDE1PYHR6CiPD01hcWcaCkPy9LdWorWtCszhmbEZsH+lBe22l2L8Rzf1i34ExXBbnnloSoJ4bFRqVuK4ZxTTTBPhEeSpyY4MQGh+LOPNDMHIWKn7xZVweGcLE/CKmRcd0ebIR9XVxsDpvicDARFR29KOrbxhXpsT5OxpRW1UjrrkHA1PLWNrAzUJQKzPrVLPrNiI1wLcgzQp71MvdDW+//hrSUpLX1m4fUgA8XgFwD3eZTcdgFzrbyCPDAuQjI3IKaFsrAXChzayT4DNCuicKSVlZh8c7V801XOmqQHVGBKKiohDtLyR8fhNabkswXMTMYCWSIvLQ0Daxtu7eiaCmg1XJXL4TqQG+RYmTNnz+0YewNDPBkPjotxPdAPgFDXi6u8rpoJkiOzgwIJklsAl0zk9nbWkuzRVVgF9fWcLcYC9GJ6dx+XG7KFYnMNJcgOzkNGQUd8qch9tpBUvzUxjoHcH0lfuv6UdA8xkp+YEBrqrnb6YGPC5SA/wmUYoxVZLFDpITE9bWbg9SAvyi5nmZLdbR0S7V8v7+Psl0ujHIpaWlCVYWZti989t1AP/xSUjN5XnMLwmgra1Rpeuri1ieE2r5/MbbH5YIaGXqLPmBAE5A80AlqwH+dNE1oZpRgu39/jv5kc+tVT3ZDkSAJ60B3N3VBe1tbbJD4wQWZI5/D/T3y9Bdzue++7vHDPCFHkzXRSEqoxUVGyX2zXdiqiEBsXl9aPwRlCuq5cymU/Jm8RB3BDhBrarnqwH+9BGrubq6OOHo4YNIiI9bW7v1aR3AXQTAWwXAhwTAewTABff3CoD3CYA3bgTwRSzODaK1qRdjE2OYGu1DW63QAGZnMSKkfm91GRrKLiErLR7Zjd1oau9Aw6UoJMenILdlFAPDYxiqzkZ+RjQiolKRVz+KycV5zLTnIC8xBKHJlaiqLkFfugGMjJ2gaxqE2OQ8lPTOY06Js+lK9KboQkvPBUYWwYi7VIrqoXksz/eju+IS4sIScKmoDQNzy5gdbkNDVhwys9JQ3FSP4px0JEYkIbOkA8NLQnNea1KViEdFyqyCHxjgSh2fzOUnTWqAryd2up2dHTh+5JBQ1fdK+3Q7kCrA3UQH1trSIu1uOtvIDHChJG8SoKYPYj3AFzAz2oBknyiUVCQjLzMcboYeSGupQlJ2AeItrBHteBEW7h4ITktETLg/HPR0YGksAOuWiDCvIKS6G8DGwwX2pkbwjohHeEEl0rwdEOhuDWuvZCTGRKMuRQ/aOma4oGUAeycn2ITXo2dqzd6eqUZPsi7OnTMR++jD3sMPDkEFqEn2QqSHGbQ1tWFp5wn/nDaURPkh2kEXZu7u8PK0g62VOQy0xPXZeiK4ZATDc7dDXAlwZX78AwNcVc/frJHHRWqAb0wMBtnxxWfSITU58ZCREU8BKQGupXkOrs6OaG5uknZ3V1enZAa4cA45VroxFyD8/rtv1qnoC+M9KHCwQlyEARxd9XF29ylYx3nBJCQL7mesEG9jAK/STjTmeyPKTgvHLMMRGe0HOzM3WO4/Bh87E7gVd6EtxwOXInTxg6k/tC5EobK1D4N9vWhN80FxijEuOF1CcmkRKvKDYWYUi7quacUFTJejK9Uc2vYZyKgqQFlxFHQOW8Jt/05Yu7rCI9IH4d7m0HPNQYi+EWIjfOGaXoBgzcOwcnITnYobApxNoO9Xj4bB2614JcAZn0/m87oT3RHgbORe9fzHRWqAb0y0T02M9PHBO28hKTFB2OdPXtt6GLoBcI1zcHZ0QIMAb6+Q2O3t7ZI7OjqE5tKJ2poamBgbYte3O9YB/NrcBEbirBBgfBJahtowMD4t1GVNnPMsgJddDNLsLRHWPIj2PFdEmJ3AfssYhMXGy/jzcGMzhDjaI6RtDKN1gcgJP4tvtV1xUusSmntn5XRXk1UxqLlkDkO/cuSL62kuj4CVQTiqO9aGvCZL0Z1uDVO/apT3tqC5Oha6e/Vg8dUXMLO3hXtiHJKS4hCZXotLVpZIiA2Fb1EJ/E7ug4WdHTwToxEXE4Po/B4MXr4dd8QiJTdTZskPDHD2Egpe3LSRx0VqgN+ZqiorcXj/D9i961vk5+Wurd2apAT4BQFwZovV19ejW6jlbW1M9Wy7AfLq6mrRsRncBnBcncW1dl84Hj6O0xpG8E2ywJkv9+OiZz6ik7ORYmmMoIZe0UmkIc1JA4cOasLEVKjoLtFwuWiFcDtbAfAhDNZ4ISXUHIcMA2F22hC+Ph7wCExGnJ8bihINYCAAnt3cirrCYJhqB6OibU17Gi9CV4oJDLyqUNTRhJrCSBgcNkHQhT0wMtTEqQt6sLNzhFtyHZIsrREbGowwoY2k258U6vk5nL6gA2trR3jnDqB/9nYVnc+HkpvJR2Rq2HeiuwKcPcXd1IDHRWqA35lWVlZRIID97ddf4MjB/eLjr1rbsvVoHcDt7VBXV4suoZa3trZI5gQQ7e1tqK6qhImh/u0AZ4b2Yg0yg6MQE5OO2p5CxLgEI62kHa29bWjOSEPZyAymV0fRXSLsbmEGBPi6wCU0CzECwBWZ6WL7NKb78lBXUYhoIWkLw9wQ5u8AKzchWaMS0VSTiMSSHrQODWOgoxQpcWXoGV2LaJntxHi9sNWFBO4YHUJvWxVSIzPRUhCB5JhAuNo5ISggCJHF3ShPyUB1aTlqJ4TWURuPxBBfuNjZwz8gBLFVYp1izod1xOczPz8vE3DIDwRw2uBKPZ+NbdbI4yI1wDcn1pfj9Mc7Pv8MRw8dRF1t7VPRMd8v3QD4+bNwFNKUqjhV8pbmZsl0unGIsKqiAsYGetj1zdcC4PVrR98kOiGVoz/XVSaO4xDjqmDFthWsLF7B9PQVzC2u4KrYTx4n9+RvtiP46hLmZ6YxMzuPJWECKdqWOwm6eZ4bpLpd/ubCdVxbEueZuYzLcytYVZ7rxo7XcG1xRs7Ycnl+VVwLj7idlABXFsB4YAlO6X1TDXjyqYlqgN+dmHwSHRmBrz//FHt2fYeiwoK1LVuHlADXFAC3t7OR2gjV8qamRsl0urW0NKOivAyG+nrYKQGuKsHvTKzQ2iyOHerrxfLS1ky35fPhe1YWwKCP7E60KcApvZV1sNQA3zpEtS0kOBAfvfs2Pv/4Q+zbs0vYsnZySO2GsHiKSQI8UQD83BnY2VpL/wIlNkFMbmoUIG9qQllZKQz0dAXAv9pQgt9KbDc40B8H9+1FSmKilIJbkXgfLFnFDDsyNe070V0Bzo+FasBmjTwuUgP83unKlRn4+XjhX//ln/BXf/VX+M0vf4r42Bix5elHOD/g5KQEqaLbWVujUqjiVMsb6uslK0FeWlIsJLgudu/8Zn1Ntg2I2mhUZDi++fJzOXlEcVHhppLvaSYFwK/IDDvyAwNcqedTDeADetKkBvj9EVMqDwlp9a//45/wxp9fhpmxIXKzs+Sw2m0241NEvLaU5EQ5H5u1hQUqysqk7V1fVydZCfKS4mLoXNDEV59/IlX2OxHVWU6k8OWnH+PYwQPy2KchcOtBiTY3O3AWvSBzlOtOdFeAE9xUA9QA33rEd1gmpFxoSLB0Vh09uB8fCrXd1NBAqrQMdX0agU4JFRkeipNHj8DGyhLlpaVSYtPZRqbzkEAvE+tZn+7lF59HuVDXNyJ+t7TnPxOmyukTx+TxT3Pndi8kAS4E78T4uCxhtRk2NwU4ez6Cm/WvqK4/aVID/P6JYFkU746hnizUaG9jjdPHj+H7b3fgxJHDiI6MfKpmK70u/tG+PnboAL796gthMweiuqpKApzAVjIB3tTYBBPRWf3qpz+RYa1MSlEl3jsdjl8JyU1wV1aUr23Z2sT7ombNyjbkhwI4p42hGqAG+PaghfkFZGVkSPuW4a10OBno6sjUU6qxHFtmHfIfixhlR092V2eHDDXt6+2RH6ySBvr7YKSvhy8/+RjGBvqiU8q/AWilBFdKcdrlSYmJOLj/B7wuTBB2XkwnpX1K31FMVKTsJKi51G7huIBbiRMvskbdyOiI5AcCOB86PXWKSpbjAuBP3uP4QAC/fhVXV5awtMi43WWsmzrs+q3jmfdDTKd90GOfPFHNq6utkSWPCAJ63Dmsxkn3fb09kXHpknRuEVgsuEC7nZKeTNWQKiI/LGUosxQGQtNjrTRKlaGhQZkUwqortHkrhPRkhF1aSoqc85vzrNFsyMpIv/GBUtOICAvDO2+8DkN9faF2l0kgE9A11dW3Mdc3CsmeLq6VUXy8D876EiWkdoCf7w1wN92Dh30rEUe0Ll+eulHCajPhuynAqQYoX+rTMKRw/wCfx5WxdjSVFKGksBBFJVWoaxvAyMJ1OWPEtek+jAz0oW/6GjiH4L3TElbnhtDdPYzhiSfvm3hQui46OGpovT3dUnLHRkfB0sJMguW9N9/Ayy/8Ae+99RecOn4UDra2snySp5D0Hq6uwkYOkw67kqIi6ZGmncsSxywlRW3AwswEGudO4/CBffjys4/xtnhv77/9poy0OyrUb84cGhzgL+uZKx1etKNPHjsiO5rIiHC0NLdIIHOY7E6slOzUPlj44Y9/+B3+8toreO4XP5W12ooK8kU/vrVj82+lZdE5szNVlrBa2ASbdwW41PMFoLYmwNtQn+EG48OaMDG2hIuHDcyNzGHpkoTivimMVoTgUpgf/CuXMXlfIyajuNIeA1e3BCTkDq6t2/pE1Zax3gx55cT7lLDMt2ZBCStzsqmsx376+HEcEcA9JcB47tRJnD11QgJZCVxmeFETYE01At1TgJ7j8rSHU5OTkJ+bK0HJDDHV74qzmLBjsbOxkjOoEryVlRWbMkFOr3q9UPc1zp3F//qn/4a//5u/xj/+3X+RIbvbcVJCal8EOP0qLNe1GTbvCnCCaWRkZIsCvBRZQTrY/aEmnIMEqMsyEWOrA4NDJ2GT3oySSDMEWujCIHsZY0srWOitQFlyJOJS8lDUPoPZtUSe60uj6K+4hIzYGCQVtqJTaAWjVQ44e84dPgntuLY4hn7xgXUMz+DK1nbQ3kYEPVMz6ejiuHOhkIgJ8fEI9POTFU/JPmt/I8JDkZOdKcHJfaurK9HX1yv9OfdCDrY2+Msrf0KM0CQIWAKYqv3duFaYGmQL0RnRo/6GaIN+hTjxvnq6u9Za3z6kAPikLFtFkD8wwDlERnAPC/uLNtaTpvsHeDlywsxwZJc1InPqMNDfjfo4L/jrnYe9AHhBhA3CHS1gnjWF3rZiFAWZw/D0UZw9L0DvlIi8DgHyuUkMV0XAz0QDWieO4qSeNwJiE1FT5gwtQ3/4BaahtTAKwe4hSKsdxuj20gYfK9lZW0mTIDU1WUpeRqqVl5fdlauEecHOgNF63+34SjrnOEHCdiX6POj4lrXpBgYeDODsJThERh2fvQQdbk+a7h/gVSgM1cHeN3fhnIYBHB30ceHIMRw/64q4RmFDpwuAu9nBKLIeOa6asLR2g0t2MxoLIhGidQzmYSVIy0pBpuNpaDqn4lJlObJDgxBgbSZUc1uc0rfBhW8Pw1FPG+axDWiaUE5ho6YHIZZAfvuN15CUlICGhnqUlpbcE1OKE+icaZSznNCk2M6TMxLgdGZyQgjWp9tM+G4KcKWeT1WAqtqTpvsHeCUKwgxw4KNTsLD3RWxqKDwMTglJfBFWSQ0oibBErI8NtHwK4HviAGwDEpHJqL/penR5HcRFl3gYmrghWOsQLLMH0C2k8/LEEAZai9FeZoVzO97HH/75BXx92BJh3UsPPRPks06cWPGF3/1G2OtBMsGE4C0Rqv7dWAlwA31dWd0lJChQmpfblZQAZxEMgvyBAE4VnQAfEOCmKrA1AV6GnHArnDzojazGMSFdr2O+JhTpVvuw2ywZQVb6SA6yhYZnHlwOHoB7XC4qeNhyH2ZjjkHPNVbY2Y7w0zwC17p5jHDb6jwWR0vRVmKL09/txpevfISzuuZwzB2S3nk1PTixguqf/+Ml2AlbvLAwXwK3uKRI8kbAJhcLe5/qOTuE40cPSw88o/T4/W5XUgK8p7vnEQBcgJvBAwwceNL0YE42Pez9VA8+8QVoaG5EQ7o3Ym1O4YhtGiIsNRHtYYkLgZWINTkBGwc3eBbVoDE/DonGh2EUmIugsEjEmxyElncmUitrURovtvlYIT7dCvsuBCDAyQW5QTo4fs4LkaVDDz3d67NMhYUFOHxwHw4d+AGRkeGoqa25AeINuajohp2enJyE3UJ6s0jE0xCU9WMSAc7RrW4WoOzt2dR83lRF5zSt1PHZS2xNgAtARmpj/+sfY8+eg8IOP4kT+/fjlIYtvPO60RBvJwDuCLvMAbTl+8JT5wgO7tmN0yfE36PW8C/sx+RsGxpjTaCx7wBOHvkBh46bwNTOGzlFrtC2iERMZgPGaiLgf/4oTMPKULZ9Tb8fnfiNBfr74sN334KRgR7y8/NQWiLsbMEEcxFjGchFhXKZ4GcwTmpqCs6dOSXHwRlEs9Vjze9GSoArC1DOXnlAgDOKjeVpGZH0NNg0SoDz5u6NruDyUBNqxIdSlJ8vVL1CFOSLD6a2G8OzK1ic6MGgeEDdUytYnhtBX00OsuKiEJ+UjszybgzOUM1bwcJ4K+pzkpEWH4vErErUtg9garoHrR2DGJpaxrWFcYw2lqOhewyjWzfu5akgDmsZG+rjq08/kfXWGP1WWloqAV1YUCBDV/mXQCe4szIzZGfw9huvyqi8pymu/scipodSyDG/nyDfTPjeFeA05Lu7uuSQ2ZMmOmE+eOdNeW0/Jt2pKOk2FwxPBVH6tjQ3yYCZzz/5SEbRubk6IzY6GrnZOUI1LxagzkRkRATsha3OmvC7vtshOwMe9ywQQ3s5dM3Ck10dDwnwHiG9ux4hwJnHylI76ZfSZO/MMMecrCxki56Y2U6FgrOzMuU2BlXkZIttYrlI9NqHhW328ot/kPNWcV9uy83Olm3k5ebI/TgpH4/jb65jyaK8HMU2/u0UD2Ur5wI/K9TS0iKj4BhPztDZC+fPwdTYCJbmZjDU08X5s6fx/XffCt4hK68ODW+vCRg3IyXAWcaK3/ODA3x8XOr4TDZgBtDDErNgMtIv4b233sAv/u1/4/fP/RK//tm/4YXfPidjiH/361/gN7/8GV78/W/wh9/8Cr/95c/x/G9/jZf+8Fu5/n/8t/8L//yP/yB///ZXim089rmf/1S2xeN+/+tf4je/+Cle+N1zeP43v5ZtsC0us/ABwyqfhqg8NW1OlOScJpm54AyTPXxgPz796H28+dor+Pj9d+V0TW4uztLB9jTEaDxOooqunF2VyTxM/LkTbQpw2jPU8dlLMOjlYYkdhbWFGQ6JHtnN2QnHDh2USQGO9nayKMF3X38la4j5+njh6KH98kXSrvLx8pQ21n/6P/4K/++//BO+EKobq3gwPdDc1FiCWvPcWfh6eWHPrp2yA/FwdYHGmVN4583XYSrUNyY2vPryH/Ht119uml6npqeLCHSaiYxdZ+JIjtDEqKHV19U+9ZVpfiwiwBmD3trcInPgZzbRrjcFOA156vlUBR4FwHNzsuV0tyGBgbI9f18f7N+7WyazcCjOTKhgzEjiuB7tbe0LmvIaaFtR8u77fqeswcXkfc5ZxbF5OlsIeHpax0bHhF1mDQc7GwHiBQF4Txw7fACDou0pYW6wDc6Wca+x0WpS09NIi4tLGBwclIUxmBP/QACnK55x6OwhqApwTPxhKSI0BB+/9w4y09PlxZkaGcLcxEiqG/6+3hK4hfn58pz7dn8vM5cYSefp4SYng2+sr5NpjZTyTFckiANEJ7Hr269lRhFtcoI4Pi5WBgKcFxKc2sLE+Jg4ZxpOnTgqO5BtR6tTmJkcQu/oIhZXhNS73IuhHqG+ja9gUfRlKxPDmBDv8uG76EWsXhnC0MQCrmwYR7KKa1fncHlmCUuPK85kZRmLE2O4vLCCu7teVzB/eULYrzP3HFJ8bWYCk+L7nFi+jnvx3KxOjWJieASTdz2B0DyWJjE1fQXT9zlsv7CwKONTWEL6oQA+Kj4KgpuNcEz8YYiBM8wW+viDd2UaIBP9CcDYmChMCumqce4MTh07KsfdKenpHSWIO9rbcObkcbg4OoBFBDnZ/ecffySdZwyhNTcxhoGejhzw52Tx+3bvkk48VguhB5aaAFU5SnaW4WUHsu1otgRV2SFwDG5E5+gcpgqd4GF4FnoR7eienkNPShjiA0KQPzGPqYU5LCyvYmX1KlYXxe/5BSyuXsM1oepeY2EMsX12TqxbvsZPELgqOo35K5idF9umOzBV7gXfiCIkl1/G3Pwilq6yyNIarQ5hsjMdMXElKKsbx4rQlK5Shb62KrWmldUVLLPwBtsXauby8qI4vzifaHtZtMOP/toqzzcn2hbrxHUpiNfGNhTXeV20o5ig4Brme5rRmJqAwq4R9Autc3lxXrQvjl9cVRT3uC7udWEWc7O8705U5CXC1yUBDd3DuLLAc9y4+jUS5+Dk/pwPQHQafVlJyAryRerwFYwui2u/ckVxbcrDRPtXl8T55DkX0ZMcgfSIMKRPrmCK0/sKMPI+5HVf5WQGa78XRzDXcQmZhU0o61hed98rnFjh2op4F/Oi3duvkSbmYL8AeGOj0G6bN3WA31WCc6oYNkIQPgyxRA9T+E4LsBKMtLuZr9vZ0S47D4YYEoCTE5Myd5iAZ9qhUmIzPpkZQiw6QNudxe/ZEbDoHit4DA4NSClPjys7ifjYWNGBnJYVRDiOv2/v93Ic/ccsR/TEaLURlZlBMDeNQVVHLUpTrHBu536ct4hB7WA1LoUFwk3fDklJQQgP80F0cS1KqmtQGOyKAA8/RBZ1orG1B+05kYiP9ICrqx9i8tg5TGO4Kg6J/vZwCMxCdkERejMMYKJvhlPnbOHlH42kWiHhlNF7k5WoCzuHY/sNYGASisL6NnTNzmNxqAptHXXIKS5BRlgQwrxjcSkxGbmZocJc84CHVxQyG0cxPj2IvsIQhHq5wsHnEvIbx8DUgOuikxmrKkVzexfahwfRU5qB8o5R+R11p4cjJigUqa1NKK4vQVaIJ0I9POEZXoTaoQlMjYj7DHGHn4sXYopSERjmBf19x2FvaQEnvxRk1IxA1eV6baINrRk+CPR2h0dsGeIdfZDoaonQjiZh/8cgyt4aHiGpyOpagJzZd6wOdcnu8PH2gVd8BZLtnJDg74LQrl7kZ+agICIaRQ2izfEJ9FdkobKpB629o5isSUZpfgSCslpRVtmOXt63txscfbNQ2tCMgfZsxPt7wc01AmmVPRhTUR8I8IGBAVkph5rwZg7wOwJceuqE5GM5WoJpYuzhpqVtEFLb1toK0VGRovNYkoUEKHlJDFzR0jwvPr4QWZ3CxckBXgLINAsqy8uxX6jrLJjHTsbdxRlBAf7SR5CclCTtdAKYPai1pbksBXRVaAtRERFS6o+OjggTYBg/CMkeHBggz7f9aA5dZVkIMTRHZpkPfFOioH3YGb6Gxsiq8YFTVCocNV2QbKMB28BQRF+KQWyAC0x0TWBnaQQ9q2C4mDgg2kEbVoEh8HM0Q2CIL5wS8hBs54KIYG/4RGQgJTIMVan60DZygImlPXx9nWHmUYSWoTWIXK5GS4I2Tp6whdYBE0TFJCJ7eEx8zH5ITQ+Fvl0w7LWsEBSWihRvK/g6m8HKNwChDkbwSKpEdEwKks0OQcfKERYeyciv7VWYFSuzmEpzF22kwe9SFqLMj8E6pAgxUTnIsdCEq5MtQhuy4RPoBzdDSwSEhMDJyAlxUW6IyQyDg1MQosU9RGdEwMbSAUZHLsDD3wcOpg7wCb6EOqHbKzTqQTTlxiDYxg4h0eHwC09FiJEtoq3PwzvFAxbeofD38kagny+c/TJQP1CPiuxo8YzsERIXDb+gFESaGMDb8Ch0PL1hF5yODC97pKbEwD+/AtFWJ2Hnk4iAqCpU+hgiNtkBtmkNiPSOQpLZYejauMDaNw1popOK8TaAsZUVLPQ1YOYSgYjKK9LcIjEUt19IcJqlDwVweuoIbjLD4ZiCl5aaIitzJAg7936YOboMJdTTvoggfz988+UX+G7HlwKI4bC2MJelfFgFhCWBvvhUEeDAulq6F7XwwdtvyiofrDCyc8fXsoImQxKpDdDBxjJB3p6eUj0/cfSwfAGsGMpxc29Pd3ncX159BRpnTyMhPm7D69uMeb/JSYlPdZTUTHM1SmzOwt/vPHRjiuDunocS29MICNLCBaFSu1gKSWBtAP+qPjQX+iDO+gwOWsUhKiEcXkJK2Rw+BR9rAbSqIfRVBKMg6hx2GXjg+NkE1PVcxuLcJPpzg1CeZoKL7jlIr61DS1UEzPUjUNG89lxW2jDRFAgbjxy4n7JGcnAI0kbHMV3pgJgYYT5ph8DGMAL1wkZti3VAkJsvwut7MJJrBa+wTFg5pSHdRVxDeLS4j0ikF1Sjjci7uoRr9V6Ij3aHprUrTE5+jzMGnjAyCILf8dPwNTsPn8pYGNn7wss1DQ1CyhfZmyBM50No+XjBJHseM0IlnuzLhIcAtY1RGCoGhlEV6IpQdy8kz9G7IOhaLmICPGBmVYSRxRVc6W9GobMtgrW+g63dUZyIaELp1FWM16bCW1MfKcWuApDCNHKvwgyuYrK1CkVOmrDc+wp27D+MoyFNaCiJQ226E7Rd/GF8cjfO64jOTzcK4Sa6yE7ShXl0gfg+E+V9e0bFITg0Ej5nDkDv+CGYRopvNdoOLm4B8EgbxdyaXU+AM3ycpi6l+GYO8LsCvEn0ENT1KRVp17Ku1i///Sdy3Pp+mGPWHKvmePRLv/8tfv/rX8jll27Z9uLvfoPf/eoXcgyb49/8y/Fxrud2Hsexbx7H8W1uY3ty7Py5XymOE8v8ze38zeOU4+Z/fH7j69uMf/Wzf8Mbr/5Jjsk+rXR9vBndQeeFdDqAE36lyGpoRXe4JsxER3kqoAwhMdlItzVHaF0vWkr8EGd5HPuNAuAdHI7I+EyEW9kj3NYawS3DGGwIQV74eezRd8MpjViU1fZhigUGSmNRl24KY78SZDZ1oKUyEpb6oShrWjN7VtswVu8Lc7sEOB03QYyvlwBwMzrSjIRUtRPtRcDWPB5tQyNoF9I13CcEiT29GCm0hntgOrwS2tCRF4wwF0Oc3XkIuk5xyLtCC1zowgsFyAzVFWaXJrRNHWGocRpnhZlgdt4NSeYaCKmIhJ5rGPx989AzMoRyJ1ME634GLaFqmwpw9Iz0Y2IgG/7OHrC1jEPT4CiaQlwR4uGNhJk1gK/mIUFITzPLLHQOjWO8vxPFnmIfjW9hZXsCZ8MqkNUzjY7CZPjqGCOtxA12QuNxcCrE0JQwZ9qFmeCiA5ezH+KQgQ6O2mWhuDoPlVlW0Dl/DheMHGF0UQNnjpvC1iYYzWnGcA3Phm9sMzrFfYe7M+fhKA699xFOHtkHfaHdBIYHISIhF3ktV7CyZopLgPf2yoKUlOKbOcA3B/jgoOwh2AgNeXrrOAaZnpYmI8Puh/Nzc+SxjFCjt5tOMkancVxTGXHGbbSr+VsZqaaMduM+cptogzXDGP3Gfbgv17MAINtXHqeIisuXkW55Yjvb4LqNru1uzKg7np8FCp9autqNkQIrnP/ylFAPy9G/MoaRMifofn0axiHlyCsrQLqNGYIFwLtGSlHoZ4DTB8/A0EATF23DYHvRHtH2tghrHcRAfRCyouxx1joaDhracLUXoHYQ6qmLK4qSTWAWVC5s5g458b2lgQB48xrAr/ditMEHxudtYH3iFNzsLuKMsRXsNL6BnqMF9plEw84iHq0DQ2iLdEeEbyiShB09XGgDz+AMOPtkINdTQ0jm89j/1SEYOMchXwBcYX5OojpAC+anjkM/JF8AbDf0DK2ha5+NDKuLCC8Pg557hJD8+egd7BMANxO2vhbMQjkCYwl3OyO4iN+axl6ws0pA6+AwGoMFeD19JMClI/v6IOpSfOBy4RxsXR1hZhcCl3NCE7A8Ddc4G1wwtYeFkQGsheps4JCM6p4alCR4wvnCedgILdLMOgheZzUQ6CXs+8w0eJpaICQ5FaERbnA4Lq43KBdepqdgfE4TJmGV6M62hW94Blw8xffF+za8gIPfnYDO4T0wND2Bo1oG0Bdap5mww2MaFrGkAnCapYwNoBR/cIALQ14WtBONjI3IbGg1PbU0i4WJOuQlFqKifgQrWMbCVDOKkgpR0zaC8clB9FaWoXl8FrPXr2C8oxz58dFISxL2eGYVCrIq0F5dhdapOcwKbaC3Q0ijml405ychKzkMwUIDyM4rRV9XKcpbRtA3MY3JkTZUlLRiZFLppprF/Hg9ChIvIT8tGQWFacJOjkNyfAQyy0WnUN6B6opOTM3OYbqtDm2NLeiamcH8YBUaWvtQWdGEFmEDp6SlIiEhG6X13RjmsN9a61ONRajJE+u7J9FRkoqKSqESN46hr7IIbSOtKK5rE9rmAGZmZzBSU462zmpUtVchNzYSKdGhSMwvRFp+g+Ia5uYx0VKLlvoGdC0rbfBrmOtvRL2w1eMTYhAWX4jc1EK01pWgcagRhdmXkCokalyqeBb1E7i8JJ5xXw2q00IRI0y/iIQiFKXlobWzHe2Xp9FTloOa5g5UNTShMScVpV0TaK3KRXVRAUp7ZjAzUIOmtl5UlTfK+04WgjMxMU9oinmors1GSnISkoR5mFZQg7qRqzeG9iTAhQSvqVbUh39ggLPekxLgz0KWzrNH17Gi1Ps2IwYGcbjrXunqMjjqJT/IB4n7X16SZa0fHV3H/dZ/uL5y5wM2ehKb7X+vdP22+16Wavmt57sJ8KqHA/hAf78ENxu59xRNNalJTT8mEeCKSreVqH1ggC8uyvFkgpvF5++9yIKa1KSmH5MI8O7uTjl0XC2wyQqrd6I7ApyD6fTU0ZAnwBn6qSY1qenJE7VrZnmyZl1VVZVM674TbQpwSnACnEXve3t6pSddwdNycF0yf0tWblvP9LxvtP7Gccp2brS30b53Yu6/dswt7XBscFp1X65XXV7H3F8xTfK642/hy2Ifycpzrh17c3nj41T59uNUWblt/T4btaPk9cdvzhsdr8q37qd6rCqrHnMvfOuxm7cxtcaqy6rb74dV23oU7dzKG+374zPnI2tpaVqrCf+AAGcvQYBTeleUi56islL+VnCVBD2ZvxW8fmI4JdfW8K/qfgpmFUzJsp3KG7zRPqrrVPlGG2SVNsgshl916/a13zeOXbsHxf5V8ph1x9/Cqvsr27q5XfX3TVZOsUPm8u3H3WTlNsX29ftUiuev2paC1x9/N964jZu8fr/bj1fy3dq5lW89VvF3430plciqy6rb75UrKta3dbOd+7t2srKdW1l1263HKLfd/H3ndm7yRm0o+OayYl8Wm2RZaT7LzSZ52FSC01PHj5kTrXNiOOVf+XuNbyyLbRuy3FZyO68dz3pbyt+37qssbH+ndTxWwcr1ty7fhdcK+nGanQ2334l5zNrvmyV8Fb/X7aey/U7rVXnj9Xdua/1+GzELEyp54+Puvx1FW5sxyyqpVj9VrFccq7pedbvimI3aurmP6jKZxRdlAcYNt6/fdyMuYiFHlTbul5XHqvKt229dvhMXFiqYv4uLbx6nuqy8Xv5W3i9Bv5n5fEeAs/oKRT8Lu7W2tqKtvQ1tba1oF39vcvsN5qR1G7M4VpXZlvy9tl2009HBNhRtKo9Zv3xz/c1j+ZfnJYvf7WSxfo3l8arHqbQl7+dGO4plxbmU6xXcLtq8eR3rt5FvtsPfLfIvj1Guu5VVt6keq8psR9EW/3LdzfNzWXmtinU3r/9me8r1irYU7SjaUh6j3P/mOuW5b29HsU7RjrKtjfdXnkdxrvWsuq1FlmNS/t64LdVjVVl5nGKZ7SjbUh53p2Nvrr957paW9W3c5PXHbrSN7SmObb6FFe3xd2srWfVY1eX125ubmfOxvq1b91Nc581lvjvO/fZAddE5+saEDhZVYEVV1n1iPbX1rJhoff02xTKPURy3npXr12+/9fgZeV6ysr1b91Ecf+v6m9vX8/p168978/6U16TkW/dZv/7W35fXrb9935vblfuoLquuV25T/L3z+W/dprru5vGqx93pHm/dT7Hv7W3f/vvm8mXxW8k3tyl4o3UKvrWtzfnu7dyprXs/x73xndq7fFnJd77Wu7HSB7PRNlUmsJm4tVmNwU0AriY1qWmrkxrgalLTNiY1wNWkpm1MaoCrSU3bmNQAV5Oati0B/z/bBYS+7dOmYQAAAABJRU5ErkJggg==)
physics-General
physics-
A pendulum beating seconds is taken from the earth to a planet having both the mass and radius half as compared to the earth The time period of the pendulum will be
A pendulum beating seconds is taken from the earth to a planet having both the mass and radius half as compared to the earth The time period of the pendulum will be
physics-General
physics-
the dimensions of (force constant / mass)
are the same as that
the dimensions of (force constant / mass)
are the same as that
physics-General
maths-
Which of the following statement is true
Which of the following statement is true
maths-General
maths-
Find real part of ![cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator i over denominator 2 end fraction close parentheses](data:image/png;base64,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)
Find real part of ![cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus fraction numerator i over denominator 2 end fraction close parentheses](data:image/png;base64,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)
maths-General