Physics-
General
Easy
Question
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that
![](data:image/png;base64,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)
and
only
only
The correct answer is:
and ![m subscript l end subscript equals l](data:image/png;base64,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)
Here, effected gravitational acceleration is
![g to the power of ´ end exponent equals fraction numerator m g minus q E over denominator m end fraction](data:image/png;base64,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)
![therefore blank R equals fraction numerator v subscript 0 end subscript superscript 2 end superscript sin invisible function application 2 alpha over denominator g ´ end fraction](data:image/png;base64,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)
It means,
for both particles are same
This is possible when
and ![e subscript 1 end subscript equals e subscript 2 end subscript](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAOCAYAAACPW1QeAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAOhJREFUeNpjYEAF4kC8Boh/APFDILZnGDhAFbfwAfElIPaD8rWA+AoFjvpPBKa5W7qAuBJNbAsQsw1ALFHFLUxA/AGIRdHEPkFpegKqucUcR/I4OgDJj2puAaXdVUSqVQPiWiC+QKOYItYtMM/+gnpYBV2BJRCfJNLSxUCcRiCjUwJIcQssaWYB8TlskteAuACqSBCaUW0JhBStAKluYYAW/RhACYgPA/EfqKHJREQ/rQCpbgHVYQepYTEtPUUKkITmKaXh4ik1aP0lSS0D/w+CGNoGbX0wDBdPgTykQU3PENuGoyXA6Q4AzBBb0aWqa5kAAACLdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPmU8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPj08L21vPjxtc3ViPjxtaT5lPC9taT48bW4+MjwvbW4+PC9tc3ViPjwvbWF0aD79iygsAAAAAElFTkSuQmCC)
Related Questions to study
physics-
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,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)
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMgAAACOCAYAAAB0WUfvAAAgAElEQVR4nOy92Xcbd3rn/akN+0KAABdwAbhTlETJWmxJ7s3d6Z6T6Uy/pyfzXuXinb8k6b8iF7mZM1czF5OTOUlPMnFPjztuy2prsyiJ+wKSIAkuIAESJPaqei8KVQQgUiZtUaJtfn1oUmSh6ofC76ln/z6Crus65wy6rqNpGoVCAQBZlpFlmUKhQLlcxmaz4XA40HWdcrmMKIrIsowoiu945d8cmqbxrj8SURQRBKHud7quW19vEoIgWF+NUFX1nZ9DPtGr3zLMhUqShKqq5HI5Dg4OWF9fp1Ao4Pf7aW1txefzIcsykiQdeXMucIFvinMpIGAIiaIo5HI5xsfH+eyzz5ieniabzRIOh7l16xa//OUvaW5uRpIkdF2/EJILvHEI58HE0nUdVVXRdb1OG1QqFf7whz8wPj6Oqqr09PQAkMlkSKfTaJrGpUuXGB4epqOjwzK7wDBVNE1DURTr3KIoHmk+nCechRlzGhxnqsDZrM281lHXPOn13tQ5jnr9udEgpt8hCAKyLFMul5mbm2Nubg5BELhx4waDg4PIskwmk2FlZYWlpSWSySSZTIaWlhb6+vpob2/Hbrdb5yyVSoBxA2pv1nkVkne9rtdd/6zWdtx5T3O9b3qOY19/XjRIpVJBVVXL2c5kMvzTP/0T29vbDA0N8eMf/xibzWZpgFKpxPb2NmNjY0xNTZHP5+nr62NoaIj29nb8fj+KolCpVJAkyXqdroMknW8tcoHzg3MjIKqqomkakiRRKBRYWFjgv/yX/8KtW7e4e/cuXV1dloYpl8uoqmqZVMvLyzx9+pQHDx6wt7fH3bt3+eEPf8jg4GCdIBgaxFSn7/ANX+Bbg/MhIJpGRVWtMO3q6iqPHj0imUzywQcfMDw8jMPhsEK6tTanGerd399nY2OD8fFx1tfXEUWRjo4OBgcH6erqwu/3IwgChUIBm812Efm6wIkgHycfZ7V5jrqejg66iihK7OzssLQUJ5lc5fLly0Q62rDZZQRBBzRLy4iiSEWtgK6jKBLB5iZ8Pg8+n4+VlQTr60kymR0+u/8pkUiEvr4+ot1RHA6ncUVda1iP6aTVv+8LIfp+40gBOUvhePV6xsZH0FDVMonEIktLC0gSDAz2EQj4EEUdQdCQJCPxo6OjI6HrFQzxEhEFCbtdJhbrItLRyubmBrMzM4xPTLC8HCd3kGU3s0Mk0kkgGMDtdiHLMpqmGu9XFxEEEUGQ3tr9uMD5h1CpVF6RkLMKhR6VjTU1g65XODg44H//67+yspLg2rXr3Lt7D4fDbghETfjWOocA6IfrbQz3qRWNQiHP1NQUjx4/YnZ2lo5IB3fu3qW/f4CmJj+gI4kSYHyJYr2ACILwncjQX+Dr4ZwIiI6mlbl//zPGJ8Zpamri3/3i3+Hz+xHF+nXUCYh1DuGVNZuRsUK+QLli+CjJZJLnz5+TzWZpampicHCQGzdu4HK6AQldFxCEemG4EJDvN2TT0X13EKhUiqRSm7x8+RK3x83w8DA+n+8bR5okScJut2Oz23A6nfh8Ppr8AeKLcZaWFnn48CGbm5uMjFymo6Mbn9ePIIhomuGfvC5pdoHvB2QzdNooJGdRunFcVjO7f8Dk5CTpTJrevl66u7rRdA1RN57ctUk+M6FowlzjcesVRRFVNfwMt9vN4NAQgWATTqeDmZkZlpeXyecLpNO7xKK9NDe3YLMp1jlrv5sCc1HW8v2BkM/ndVmW60o9XhcC/SYbo1KpWOcwN5mqVliIz/GP//gPeL0e7t69S39/P6qqYrfbkWXZOt58vVlGYhY0mpDlw8IATdNQVZVSqVSnCcwIGBglKy9fvORPX3yBJNno7xtkdPQ6kYiRjRdFsU5IRFGsq/u6EJLvPmQzt2BuhtqnfKOd/003RLlcNi5aFUhFUdjc2mR2dpbd3Qw/+tEPaWtro1Qq1WXVTYEVRRFRENEEDVVQ69ZpJhsbUStAxsHGl6qpeNwe7t37kJbWVl68mGBicoLHj59w79493nvvPSKRCLIsW1n+C8H4/kEuFAqIomglz2qF5E1vBPPJbQpjsVhkZmaGubk5ent76ezsxOv1omnaK4WFoiAiSBK6rlEsFSgWCzidzjrBbkSjhjF/JwgCgi4gSAJOh5Oenh7cbi9dnd0kEqs8f/6c5eVlLl26xOjoKMFg0NJimqZZWu0C333IiUSCvb09mpub6ejowO/3n5mNbW5WsyAxkUiQWE5QqZQZHR3FbrcBVUHS621/AF3X2N7ZYX5+ju3UFv0DA7S2ttYJSi2Oi0CZG934ruJ0Omlva8frbSIUaqFcLrO2tsb4+DiCIPD++++jKId+yYVwfH8g/epXv/rNo0eP2NzcBMDtdlumTe3mel3X1klhvt70IR4+fMjGxjrtba3cu3eHXC5vCI8ko2oammaYWZJoNE5l9/cYH3/JH//4R8bGxqpZcQFFkbHZ7JYpZuTDjZBtbY7E/FJV9dDnko1zl8sVdB28Xh/9/f2IokgqlSKZTBKLxXA6nZaP84rZdoHvLKS//du//Y3f7ycej/Pw4UOWlpYIh8N4PB7rqVmbgHu1+O/kIWKzILFcLrO9vc2nn36Kz+fl1u1bhMNhVFXDptiQZQVd0ymXVRTZhihK5PJ5pqam+T//5/dsbaUIh1twOJy8fDnOwUEOn89PqLmtaiZWn/SigCSKCGK9gIiiiCIr2KtCpaoaCCKybLNMzaamJhRFYX9/H4/Hg9/vx263H5lzucB3F7KiKAwODuJ0Opmbm2N5eZlPPvmEcDhMLBajr68Pr9f7Wlv/pEJibtD9/X0+++wzXC6X0cPRFqFS1rEpDgRBRFUFdF1CkgREUWFvL8fMzAz/9/f/RmdHlB/98CM6OztwOJw8ffqU9Y11/u/v/43u7jhOp4O2tjbC4RAulwMdqPmftY7akisjcieiaQKVskqlUsHj8eByucjn85RKpSNDyxf47kMG8Pl8DAwMEAgEaGlpYXNzk729PcbHx1lZWSEWi9HR0YHP57P6xL9ONawgCORyOVZXV5mYmOD27dt0VwsIjXParGONng2NbPaAeDzOy5fjKIqNK1euWtW9yeQ6u7tZ9rMHOJ062ew+a2trbG1t09vXw/DwIIaReLwAG+FbAVXVUSsq5bJqBRD29/fJ5/MoivJKOcsFvh+QRVG0WlPb29tpb29nd3eX2dlZpqammJiYIJVKkU6niUQiBAIBnE6nlSeAkz9RdV1nY2ODmZkZVFUlFosRDoeBo+x6AVHUWVtbIx6Pk8nscvv2+wwODmGzOVhZWePRo4ckk0lCoRC9vb0EAgEeP37M/Pw8kiQyPDRoNUm9TkjMfEy5rKJpOrIssbKyQjKZRFEUy9y6SBR+/yArikKpVLJyFIqi4HA4uHbtGsPDw6yurvLpp5/y29/+Fp/Px+3bt/nggw9wOp2Ww3sSp1UURSus+/LlS+7cuWO1x5pJv0Zomsbu7i52u52bN29a0aS5uTkePHjA48eP+fWvf83o6CihUIhSqcT8/Dy5XK4ugiUI8Dor0PibgCxL2O2GtpiYmCCRSHDp0iW6urpwOBzWmsxQ70WN1ncfcrlctnosJElCURTK5TKCIOBwOOju7ubf//t/z8bGBisrK8TjcWZmZujv77c2j6mFoL70oxFmaYfb7eb69et4PB7Lr6kVMjMMW6lUGBgYIBaLIQgCdrudtbU1nj17xtLSEn/+53/O5cuXCQQCbG1t8fDhQ6anp+nv72doaKh6HhAFI6ql6fVrPISOJAqIggwIvHjxgvX1dYLBINevX8dut1taw4qUXWiQ7wVkk1cKsEK7tfkKSZJoa2sjEAgQDocJhUIkEglSqRRffvklGxsb9Pf309TUhCzLdYJhCo2u62SzWaamptB1nRs3btTR9TQ+ic0NKMsyDofDMmvMhGZbWxs2m40bN24QDAYtk3B+fp5YLEYwGCSRSDA+8YLW1hB9fX3V0nYaNMvhRhclEbUC2WyW58+f43Q6GRoaorW11Vpn7esvBOT7Abm2fslE7YY1zR+Xy4Xb7aatrY1oNMrk5CSJRIKtrS3S6TQ9PT20trbi9XqtDWUKSKlUYmFhgWQySXt7O9evX7eiYseZKbUlJrWb0efzcfnyZVRVJRwOk81mmZmZYX5+Hp/Px61bt9jd3WVufo6VlWXS6RSSJBKNRvH7/dZ1G4scRUFgP59jcXGRzc1Nrl69yuDgoMWQUruGC+H4/uBI2p/a6t5GYRFFkUgkQjAYZG5ujidPnvDb3/6WSCTChx9+yLVr1/D7/XWFiQcHBzx58gSbzUZnZyeBQMAy4xqvV4ujhMdms+H3+61MeCKR4OXLl5RKJf7iL/6C1tZWZFnG6XTwwfu3mJmdYn5+AVVVuXnzZt25GuvONjY3+OKLL2htbWVgYIBwOGy95wt8P3EiXixBEKhUKpavIIoidrudgYEB2traeO+993jy5An3799nbGyMGzducOXKFXw+H/v7+ywvL5NOp7l165aVpf66PSim2Weuo6WlhR/84AcIgkBLSwt2u53Ozk40TaVSKbG9s8n29hbFYhE4NCPBSFwa7wv29g6IL8RZXFzkL//yLwmHw99onRf4buBEAtIY1jSfqi6XC4fDgdfrxeVyMTk5ydLSEg8ePGBlZYWrV69is9msMpZwOIzP56vTLqc1Vxqf+k1NTXg8Hut8qVSKg4MD0pk0GxtrLC/HCYWaCYVCxut0w2GvDQQAxOMLVs6nq6sLp9PIzVxoj+83jjWxGmFulMYCQkmScLuNLsCmpiaCwSDj4+MkEgk0TcPhcLCzs4Msy9jt9rpEo/mENs2lxpqp1z29zdeZEaZUKsXy8jLZbJZiscjBwT67e2l0XaW7O0okErFe28ignk6nWYzH2d/f5/33PyAYDL4V7fFV789s9DouKHDhC509jtUgjTe/VkBMx73xGKPEI8y1a9d4+PAh4+PjpFIpRFHE6/WSy+UolUpWTZOZRzHNN6DOfDquhN0MK5t/z2QyPHv2jN///vc4HA5aW1tpb2/j8sgIvX0xQs0hFJuCVt1wFfVQg0mSRDweZ3tnB5/Px9DQUF3l7lnhdWU75j0uFovWaAdzTY24EJKzxYk1SO3fXpcYlCQJn8/HD37wA/r7+5mbm2NycpLV1VUePnxIuVxmZGQEl8tlNSKZm6BcLtdpqNr6p0bUmj42m83KpmezWSKRCJcvjxCLduNwKgiiQX8iSsZrFFGxOhTz+TxLS8t0d3UxMnIVt9ttXf9thHNrhcQUDLOoU1EU62HRmEy9EIy3gzMhrzaTem1tbbhcLlpbW0kkEiwvL/Pw4UOWl5eJxWJEo1G8Xq9VxvF17H1d13E6ncRiMbxeLxsbG+zs7LCysoLf5yXiaj0mky5QLpXZ2NggldqiuTlMIBDAZrPVdSeaGu0s0KhBaluJZVkml8sxPT2NoigMDAxYvtZF4ODtQfrNb37zm7M4sdkya7KJhEIhAHK5HNvb22xubmJm8c2cR20X4Wk2gSRJOJ1O/H4/TU1NVmVAU8CHx+N+9WmrQ7FYYGNjg+fPx0iur2NTbNhsDqBeQ56lJnkdUUY+n+fly5e8fPkSXdfp7u62yl3MdV1k9M8eZyYgtURvYCT4Ojo6aG5uRtM0VldX2dzcZHd317K1FUWx2llrI0hfVRxYe5zX66WlpYX29jZ8Pq/BqyU0bEQMp35qaoonT57g8XiplFW2t9Nks1lrapV53lriiFe7HPVjf1/775PAfFDk83kWFxf53e9+h6ZpxGIxenp66kgpaoXjQkjODmdKXl1LdCCKouWMm/MHX7x4wdTUFNvb2/h8Pq5fv87g4CDBYNCKdJndf2aBYO3GNVFL2nD4xAddVwG1TkAEjJzO06dPefjwIQe5Az766COcTg/JtQ0mJ6cpFov09fUxODhId3e31YZsssrXMp6oqkqxWEQQBGw2G4qiWMe+jiGmVrDML9MPm5iY4F//9V9JpVL8+te/5r333qsruXndR3ahVb4aR93D4x42ZyogjawotQWNuq6ztbVFKpVic3OTZDJJMpm0IklXr17F5/MBh4JWO+ejsbOxNqpl/N0QkELxAE07DATIskwqleLBgwfE43E+eP8DBgeHsTuc7GcPWFtdZ35hnnQ6jSAIhEIhBgcH68poAJaWlojH4ySTScrlMg6Hg/b2djo6OgiHw1br8lHmoq4bg31MYTLfmyAYhZJPnz5lfX2dmzdvEo1GUVWVdDpNKBSy/DrzvMeSUlwIybGorRE0cdx9O9MJU697coqiSDAYxOv1WkWQoiiyubnJxMQEBwcH1oYzOxpNx/koDfK665mv03WdcqnM/Pw8u7sZWltbGb50CY/HhywpOOwuPG4fbreb5cQym5ubbG1tkclk6OrqIhKJ4PV62dvb48WLF2xtbVlBglKpxMrKCnt7e2SzWfr6+nC73XUFmYdEEa/Sp6qqyuzsLJ9++imLi4s0Nzezvb3Nzs4O+Xze6p9xuVwoilInXBfCcHqcVC+81RFsjZvDNEFsNhvBYJC2tjampqaYm5tjfHyceDzOwMAA0WiU5uZmq3CwEUcLhvFdURQEjGpddEilUszMzCAIAkNDQ/j9vmr0qIIoyrjcLmI9MVpaW9jY2GB2dpaJiQn29vbY3NzE6/WSTqfZ2NigubnZavpSVZVEIsHOzg7lcplgMGjlL3RdtyJ15nprTcVCocDW1haffvqpVfEM8ODBA6PXPtRMOByuE4rTNqtd4OvhrQ7QqU2CmT4FYNnxZmtrLmdU1X788cfMzc3R1tbGT37yE27fvl3XuFSbfX81+mWwxgui4b+gG6XsD/70gLm5OUZGRrh37x6KoqCpGpJkQ5IUdF2wImuappHNZllYWGBqaopkMkmhUMDtdnPnzh36+/utrDsYCct4PM7c3Bw9PT10dnaiKAr5fB6Px2MRYZjEFebPS0tLfPzxxzx9+iWjo6N0dESsIMZf/MV/YHR01KJDNYMXjZUNJi5MrK/GUbPo34mJ1YjaBTRu8NoIlsvlIhaL8R//439kbGyMmZkZfve73zE9Pc2NGzeIxWJW6XqxWLS0US1dkZEIVKmoRURBpFgqsrKa5PnzcaLRbjo7urHbnIiiQEVXAcHSOrVPaY/HY/kg+/v7VCoVnE4nweYgLqcDXTfadAVBoFjMs7eXYXNznf2DPZaXFymVSuzt7eFv8nP92nW6urpwuZwIgo6ORjq9zfz8LPPzs/z0pz/m2rX3KBaLbGwkaW9vxe/3oCiicbwOhsth3jsjGFHLQHEhHCfDSe/RO5ly22hi1OY/zC+Px4Pb7cZutxMMBpmenmZzc5PPP/+ctbU1hoaG6Orqspz/SqViaRDTqdc0DTQRQZZJ72wxN7tAsVgmFu2lrS2CIMjo1sxCEXPKVO1aTHvfzPwb0SbJ2uC6XkHXYGtri9nZWZaWl9C0MpnMNuVyAZtiQxA0EolFioUc2ewlhoaGcblcaGoJRRHp6orwk49+yMjICKHmMLNzs+ykU/T29uBy2RFFHV2v1AgEHPbYvzoV6wKvx3HCcdTv36mA1P678e+mFujo6CAQCNDR0cGzZ8+YnZ21HOTLly/T3d2Nx+OxuhlrfRxDC8ioFY21tXXm5hbo7OimqyuGzxcAzByLVCecR2XO6zPqGqpaqn6vsJ/N8uLlGJsbm4iiQFd3B6urq9hsMm1tLTQ1NTE/P8/6+jpT02B32Ojr7asWejoZHOxncGgAXdcolUoUijlKpTx+vxe7XQFBR0DnMDahcygUFwJyWpxGw55ZovBNwIw+KYpCc3Mzly5dorW1lbW1Nf74xz/y7NkzPB4PgUCgLgRrfjftdbM9OB6P88tf/pL29nbL4TVxctu96kdVn+i5gxwTE+N89tlnxKIxfvLjH9Pf109iJYHT6aS3p5fr16/T19eHzWZja2uLtbU1wuEwLrer+iAASVRQ1QqqppLL5SgUCkSjUcLhMA67w1rjIQRA5EJAzhbvRIOcFIIgWGwrpo/R2dnJr3/9a27cuMHDhw958OABExMTjIyMcOvWLauH3Hw9wPLyMoIgcOfOHWKxmFUi/3VgJgFBo1jMsbq6wvj4ONFolFgshqIopFIptre3aWlpQVZsiKINl1PE5/XhcrksUzEYMBx8h9NBZ2cXzcEgiqLQ2dlJKBTC5XRVcx61ptUF3ibOrYCYZlbjPA673W4l4nw+n8UGOTMzQyqVoq+vj87OTpqamtB1Y4b65OQkHo/HauBqzJqeTlgERFFCECBfKJDO7FAoFhi9Nkp7ezvFYpGl5SUkSSIUCuH1eNjbyzAxOcHS0iLb2ymrHi0YCFq0qMvLy0SjUXp6emhubja4gCXZiMVph9RKxkTgi/Du28K5FRDgiNDtYZLQ4/Fw5coVurq6mJqaYnJykvX1dbLZLCsrKzQ1NSFJEuvr61QqFVpbW4lEIq+MVzttIaIggCgKCIJEoVDg4OAAu91OpD2Cy+ViZWWFRCJBIBCgra0NQYT5+VmeffkUWZHxer3YbDYWFhawO+x4PJ5q1GqdYrFoUS8FA0EEQURTK5hTTyRJQtf06lxf4UKrvAWcawGBV8OWtWFcAL/fz/vvv8/w8DDxeJw//elPjI+Pk8lkEEWDzeTevXt1jVC1IWab7ZDu9CRZad0ay6BSLBYoFos4HA403ciZbKWMzPv169cJBALs7OzwbOwZhWKBH9z6AS0tRgIyk8lw7dp1YtEYhUKeL589ZWVlldnZWQRBxHPVh6rqaLoK6MiaUYem6UZORxf1CwF5Czj3AnIcajey2do7NDRENBq1uH8nJiaswsjaiVVmF6MZHq4tqDTPfXwo0Ly2kTcpFAqsra3x5MkTJEkil8vR2trKlctXyOVzrK2tkc/nuXrlKtFoL6BTrhhJQqfTgcvlxuM1qIxyuTzpdJrx8Zckk2s4HA5aWlqIRCK0trQCApIov/L+L3B2+NYKSCPMYkSbzWYRSnR2drK2tmb5KT09PYyOjuLz+awsvplHqc2lnGROo1atvlUUhUqlwtzcHG63m0gkwsilEXw+P5tbW9b4hJ7eHmw2mfhinMnJSfb29rDZ7EYCc2WFL754QCqVsqp6zaFGW1tbxONxWlpaaGlppbWlBZ/Ph2KzgX6hRc4a3wkBafQlXC4Xdrud5maDzWRiYoKNjQ0WFhbY3d212OqD1aiR2X9iRszMcvavekp7PB66Orsol8rk8jm8Xm+VFaUbgHR6h2KxSDAYtEjuVldX2NnZoaWlpUposc3s7AzxeNyKwJVKJctv2tvbs0LDXZ1dKIqM0+VCsTmqmu8s72xj8OL7J43fCQFpJHgwI182m42BgQF6e3tZXV3l2bNnfP7556ysrHDp0iWGh4dpbW21ciKmA1/b+tooJKYPIiDQ1BTA5XTT3R2jWCxgs9txu1zY7HZKxSLpdIZisUh7ezu6prO6ssrOzg6BQIDbt28jCJBILLO1tUlnZyc3b95ib2+PlZUExWKRq1evUiqWGJ8Y5+XLl6wlV+np7aFYLGNTVERRQNfre9X1ag7xCA6Uhu/1MO+fKXS1vSdmOYsgvBrtO/56x+HblbeRj5oMe164Z48qKjsJzJ5uSZKswsPOzk6CwSCXLl3is88+4/Hjx8TjcT788EP6+vosE62WUcVMNB5d2KagyDYU2YnL5auWrJgbS6MiQqUskM+VSaV2ePzkMZOTk0iSxKXhS/T1DfDo0ReMj4+jqhp3797j8shVpqYmSCbXjElXokxHRxsOpwun08mLFy/Y3t7GZrPh8/poagricDiQZcXonESnoqrVvEnj5yeCfjQHsqlBzYYzSaLmHlQOKxswHw5GJM94kBhvvLEm7JhPprqOV2vHzsN+OwrnWoN8k2Re47/NIsiuri5++tOfsry8zNLSEv/8z//M1avGUJ729va6CbamVnlVi5gfqPFlCEZ9Ob9hrgns7WXZ3t5EkkWam5sZHh5maHCIUqlIKpXC5/PR3dXN4OAAqlZmJ71NpVIxRkM47GR2d1hcNBgfzZ6RyclJEKCttZ2Wlhai3d20trXhcDgolYrIiowsNX60hgAdtYkbWTMFAXbSKdaTa+yktwkEg7S3tVl9OQCqCmr1vR6W4HzVJhePXcN5xbkWkDcJU0gcDgcdHR243W7cbjeqqpJMJslms7S1tRGLxY5kdG+EUcFbL4gGjZGGIIAsK3R3d5PL7bOxuYbP52VwcIC+3j5cLhfLiWVrxEIkEsHn9TI3P8fe3q7ly5RKReLxOPH4Avl8nmAwyM6O4dfY7DYODvaZnt5hdzfDQCFPb2+vJaz1/oPAq/7EYdWy2R4siiKFQoGlpTjPnj1lObFIsVjAbrfT2tbGQH8/AwODhJrDlmlXfZQce42GK5704zo3+N4ICNT3rnu9XoaHh+no6ODJkyeMj48zOzvL9va2UVUbCuF2u48hbDP7Wo4SENViWRkcHMTjcbG+sUZnZzvhUBibzUYmk2F1dZVMJkMoFMJmt5HZzTA5OUmpVKK7u5tIJMLKygpTU1PkcjmjlTcUZnx8nEAgYFQL+JsYez7G0tKSNVextbUVSTw5TZHRFlBBFEXK5TLr60n+7d/+wNjzLykW8zQ1Bdjb22VycpKVRIJcLs/IpVG8PjdOhx1Zlq25K99FSH/913/9SrHiebEJz6qXqza0a7fb6evrIxQKsb+/z4MHD5ifn8fpdNLc3Gz1fzeuyySSqK8cPkximqaax+OmrS2Mx+uxcjAHuQPW1tYMcojePpqbmxkfH+f+/fuEw2FGRkbwer08fvyY2dlZ2tra+Oijj+jo7CAej+N2u7ly5SpXLl8hEAiwv59lfX2dg4MDIpFI3Xi86jumvrixHiZNUjqd5vHjJzx58oj3b9/iP/2//4lf/vKX3L17F4/Hw/Jygi+++BOLSwt4PEapjzlp7GSf1atrOO8+yLkQkKNu7lk2Ot4YTgMAACAASURBVJpOp5nHkGXZevp2dXWxv79PIpFgdXWVcrlsdQLWTtKqXWPt4KFafi9DgLSqf6JVHV5j4+7t7ZFOp9nP7pNcS7K4tEh3dzeXL1+mqamJ9fV1nj59Sk9PD+9dv0EoZFQxz8/P4/V66OrqRJJl3G43hUKR/f0slUqFnp6eOmpXs9dF4NBnql2/yeBYKpWqo+0+p7evl2vXrtLe3madw2g5iNAcbLZ4Aza3NpFkiUAg0ECYcdSm1zGE42ghPe5zetd45yaWeWNfRzP6pnFUDZbL5cJms1mNWktLS2xvb/P06VMSiQR9fX10dHTQ1NQE8EoGvnZTmE9vI9lomGKCfjjCzabZ8Hq9OBwOstkshWKBUCjEpUuXiLRH2D/YZ3Z2Fk3T6OrsorW1lVKpyMpKAp/PS2trKx6PB0kUsdnsBAMBfD4fu7u7r4Snjft7tGNcWxC6vr5OPB6nUqlw/do1uru7cDjsVCoVZFkmEAjgdrsJBoOEwiGWlpbYzexy//59VlZWqqMw2nG7PZYPZEbGTO0qidKRsnEcDc95EJBzq0HOEkeFsc0PSVEUIpGINR9kc3OT1dVVdnd3KZVKVjGhubnMczUKifU7UagWOFKXoTfNNEVRaA42G2Uy3VHsDjubm5tMT0/jdrvp6+/D5XSyvp5kfGKcjo4OemI9BINB43yyzN5elnR6h1wuR29PLx63xwgyUENqpx92TTa+b1VVefHiBYuLi7S2tnHnzm18fi+SdKgZTY1rBhDa29splUqsrq6SSBh5m0q52r8jG5zC6DqaqlFRqw8TRONLOBnF7HkYPfHONch5Qa0foWkagUCAW7duMTw8zPj4OJ988gnPnz8nGo3ys5/9jK6uLrxer5VDOO6hIgoCgiig1+Qg7DY73V3ddEQ6KJVLRr5FEHE6XRQKeQRBMChb/X4kSWItucaLFy9YXl7m2ug1mgJGKX9FrVT78gsU8gUASqUiqqohK4IxuFTTrF77xuWZDPIHB4ZPJIoiP/zhD7HZ7NVckmIFKczenFKpRLFYJBwO88Mf/ZD+gX4rAXv//n1GRi7x0Uc/JRaNYbM5UGwSompwB2haCUUWURT5rT8Uvy4uBKQK0+k2n/CmE2+OxO7s7GRhYYGZmRn+x//4H3R3dzMyMkJvby8+n6+O+fHVFmLRMjvAyD7X1n7ZbDYEBFStYhVS5nI59vf32c1kyOfz7O/vWx2VdpsddJBECbViMMIUigVKJUPYKmoZWTXWYeRDTAE9JKYw1mWs88svv+Tg4IDOzk46OjrQqVAul6lUqlpPlEA8bFozk8t2m52OSAdN/iZGRkaYnZ1lcXGR//7f/zudnZ0MDQ3T39dPS0srNptApaLWKbD6CoDzKTDS3/zN3/ym0TR42yZWbQPT2/xqROPgUMtnsNnw+Xz4/X58PqMr0MgXLLGwsMDBwQEejweHw1HXzXhoWxs+gGFaGBvVzEDLkoIkygiCiFrR0HSdfK5AOpOhVCyTzxeQJJlIpIPr12/Q2tKGzWa3zqHrkN3fZzezSyazS6Wikt3Lki8UDTI8h6uugtmIsqkIAuTzORYW5hkbe0awOcDwsMETViwV0bQKZjjbMNW0usoGURSRpcPKg6amJpqbmy2G/Ewmw9raKuvJJAcHB3i9Huw2e80oB4wWY9WoqhZEwbimroNQ1bxCfVDhXUD6zW9+84qAwNuLIJwn4aj1TRqZ5s1JWqFQiI6ODiRJIpPJsLGxQTabtTaPOUmrVgsZgmJk4M2nuKZpSLIpHBKCIBoz3UXjZ1GScThcuN1eIu0RBgeH6Yn1Yrc7EAQJMHrZRUmqaiiRSlljdy9LMrnO1tY2hUIJj8db3ZQqqqYiSQKapqLrKts7KR4+/BN72QyXhofo6++lopZR1XK1KezVJ3ytY2+GtEtlg0bV7/fT2tpKOBxGEET2s/uktlOkUluUS6Uq9auEJInWOlRVBUFDkgRUtWxF/STxaJ/pbeOtEsd9l6DrOru7uywtLfHixQvi8Tjt7e1cvXqVS5cu4XA4aor9BCuBaG66WhLsxvOaT3vDbtew2Wx15NW1MF9fLBbZ2dlhenqasbExVldXcTgc/PSnPyUa7a4ypEjYbAqarlMqlpidm+Uf//EfGRkZ4ebNm3R2dlIqlazz1gqI4ZPIVptAbfTRHHxkvlfDFLOxnUoxOTXBs2fPSCQSXL16ldGro8RiMaOlWFYwzU5JliiVS+ia8TBSZAVBsGFo3HeHCwE5JczcgTnbRNMMqp6lpSVevnxpbcw7d+4wODhIU1NTnXlTywfWqM0aw51f9dEcFdItFovMzMwwNTVFIpGo0ro20dnVQU9PN5GOdmTJxmJ8kecvnrG0tMTPfvYzIpGIFeo2Q7ONrC+1jI61azSPrz1WlmU0DcqlEul0mumZKZ49e8ZuZpeWlhY+/MGHDPSP4HI5ACPIoWqHyVcBAVk2teW70yLnmvbnvKI24qUoCm63G4/Hg8/nw+FwsLe3x/z8PFtbW5RKJVwuoxq30YF/na/XaPId1w5c6xeYIWjTFIxEIgQCAZLJNRKJZba3U2iaxsHBAfML82xvp4xym0hntdFMwG6zWxXQjV9HrbfRJBVFEdH8XVVQHA47Pp+PYDCI3WFnd2/X4juWJAGny2C4FEXp0LQTRETBLBy9EJBvFWoThObGsdlsNDU1EQgEsNvt5PN5dnd32dnZYW9vz6D3cTjqarsatUdtH8pJcgDH+VY2mw2/308oFCIQCJDNZtlJ77C9vUU2m2VxMU4qtYXX6+XWzVvYHfaqX1D1K9BfEYqjhKPWYW88znTuzb+7XC5rPbKsVEdfbLK7t0s+n0fXdex2h5FDESVLSAQuBORbhdqgQq0Tb9rebrebzs5OBgcHMWmHJiYmyGazOBwOS0hqX2sKRu3AoaOYJ2s3oPn6xtF1cFiVIEkSDoeDpqYmnE4HxVKBzc0NxsbGsNuN8HVffx+AFaJWNbVukpV53Vonvdb/qBXoWiGqNf8EQUAURBDA6/URiUTo6upia2uL+fl5FhcXyefzuJwunE5XNRHLhYB8W/FVkTFBMDh9zfkmNpuN8fFxwwbf3SUYDNbVL9WiMZdy2mhco2YTBAGn00VbW4RodwyH08bOzg4DAwPcuHEDh8NhaStLCKgKrn5ovh1m5KkjvThO29UJjGCuzeRiFvD7muitFmpmMmnu37/P6uoK/iYfweagERgXpGrm/UJAvnMwn+5mVXBXVxcAyWSS+fl5isWi1TtvhksbNcGbXIsoCuztpfnd//kYr9fLyMgI0WgUaJi0RI3Tj1FHls/l+PTTT1laWjY0UiCIJJpM+iefTmw638brJKt0JdTcjM/nY2Njg4ODA2RJItIWQZLMmSoXAvKdhSkkJhukOf9ka2uL7e1tCoWCVU38Os3wTbG/v0s8Ps+jRw8ZHR1lcHDQqgCohbmBdXRUVSO7t8ejx4/4v7//hERimWKxRDabpaJWUBQZhxmqPsGSzTktYCQJi8WClT9pbg6h6zo72zsIgkBPrBdFcXDSuq2zwoWAnDFqI16hUIju7m6am5tJJpPMzMywtbVFpVKx+k7OYi67pmkkEkuMT7ygXK5w79492tvbq/b9q+Fks5tyb3eXmdkZPv74Y1Lb24BIqVRkcTFOLrePw2HH6/EaiUrx9RJi5oI0XUPTDX8rl8+h6RqyIuNxewk1h1lfT1IulYlGozidnncuIBe1WG8BZq7AzLL39vYSjUZ5+fIln332Gf/rf/0vPv/8c/7sz/6MkZERmpub615rojFReJymaTymUMizuBhnYWGBu3fv0tJi5ELK5SJaAysKgpHNL5XKTE5O8r//9V+QZZn//J//P4aGhiiXyzx8+JCnT59SLBYBjBL4UAibzVaXMGxckxXQwPDRvB6vFe0qlYsUijlUzQhU5PJ5gucgRScf1YdxVmr++4jGSFftzwMDA/j9fhYWFpiYmOB3v/sdL1++5MqVK4yMjBAIBA5DpjXkCK9O9H31s6rVXDMzMyST6wQCAXp6YkgSFEsFdE1DlAy2EsxNrUN2P8ujRw958uQJoijxq1/9P/T39aPYFJLJeZ4+fcrOzo41Xq5YKPHejWsMD18iFApZ62qEqR01VTPqvVTj+rIkowka4+Pj7Oxs09HRSTAQOB/l7kdFUi6E483iuByC2+225rD7/X7i8Th7e3tWFtwgoesiGAzidDqt1x3F2tL4sylY6XSaubk5CsUCvb29BINBQLdGY5vUSDpYhYQrqwkWFhaQZZkPP/yQkUuXsNntzMzM8PTpUyRJ4s6dO7S1tlOuqMzNzvD8+XN8Pr/VUFbLeVx7H8AYqGpWCYuShKpqpDNp4vE4HreHaDSKy+U+F/vwwsR6R6jVCsFgkKamJi5dusT8/DwTExPE43FSqRSpVIpoNEpbW5ulUeB4zXHIbSVZlKgGe4qfoaFBHA47+XzBKgcxk3KmtgEo5As0NTXR19vH+x+8j8PpYGlxiSdPHrOwsMCtW7e4e+cu/qYgybV1MultVtdWKZVKlgl1nJkFRiDALPEXBIn0QYalxSVyuRyDg4P09fZXteW7pwi6EJB3gMNapcNqX0Ew5jJev36d4eFh1tfX+cMf/sCTJ08YGxtjcHCQH/zgB/irTVRA3WhpE7W2fj6f59GjR+i6TjQWI9odrRv/YNVW1SgkWZa5cuUKV6+OGvkYYHdvl3/67T8Rj8cZGhrmF7/4c+x2hdT2FrNzk0xOTfLRRx/R29uLw16lRBVfLaysfa+KrFT/rZLJbDM5NUl7ezt9ff2Ew2EOF/VuheRCQN4RahNwtRsHjE3a1tbGL3/5S9bX15mZmWF6epqpqSmuXr3K1atXicVilnlUC5PBPpPJMDExQSqV4oMP3qe3pwdV06hUynWZb1EUrSe+CbvNQaVSRq1UKJVLrK8b/kssFuPmzds4HW5y+SyPHj7i8eNHBINBBgYuEQy0AEbZuqALVbbH+vdcu95SqUQqlbJ64d9//31aW1qNqgJNQ34NgfjbwrkWkKPs7ZOi1hT5uud93TneBGprmRqvqygKwWAQt9uN1+slEAgwOzvL/Pw86XSa9fV1Ll26hN/vtwaYmq8tl8usrKzw8uVLuru76enpwef3U6lUAEPzSKJ0WPNUsx6jULFqwomGpgsGg9y+fRuv10tLS4jd3TR/+uJz5ufnCYVC3Lp1m0I+x9jzZ2QyaTS1Ql9/n0XQbQqidT0dRMHwd5aXl1leXqa5uZm2tjacLidY5HfvHudaQL4J00lt1Oiov51EQF53jjeFxuRgrWYBcDgcRKNRWltbaWtr48mTJySTSR4/fkw6nWZwcJD29nY8Ho+Vkd/e3iaRSLC7u8vPfvYzQqEwoiCgqhVEUbAc5KPMs1ptJomSNUouHAojiALFYpHU9gYzM9PYbDZGR0e5NnqN+fl5ZmYmWV5eNnI+4ZDVXWiV94sCki5ZY+Q21jdYWVmhWCxy+fJl3G43kiRWk5XSuRCScy0g3wc0CsZRvzcqXe0MDw/T2dnJ2NgYn3/+Of/wD//AtWvXeP/99xkaGsLv9yMIAgsLCySTSTo6OqrE3ALFYglJNuqhzDordBCqRNKaXu8P1QqtIAhWCYqu6eRyObq6uujo6GR4aAib3UZzc7M1/9HQNC3WsNRa06q2OPPho4dsbW3R3d1Nf3+/oW1MruNzwgJ/ISDfAui6QQ+az+dRFIXr168Ti8WYnZ3lk08+4b/+1/9KNBrlV7/6Ff39/daIt8uXLyMIQpXDqwKCSR5dry1MvK7URUdH13RkRSYWixGL9hqmmiRSKpWwV4seQ6EQt2+9T6g5hCRL1jXMxrJCIU+hUKBUKhOPx4lEIlweuYLfF0QUjX70dx+7OsSFgHwLYNrwdrvdqvQNhUI4nU4cDgcvX74kmUzyz//8z1y5coWFhQU0TcPn81U7BAXKZa2u88/8boaFv6oxqvbJryhKlTiiWtaui6ytrVWH/rTR09ODzWZHR6t7nTFOwsjSj4+PEw6HqyZiG6pWoaJqyLJUZXjRq81T8js1tc61gBznP7zN652knOOrjj3N9Y6DKSBm2YrJJHLr1i1aWlqYmppiYWGBRCJBKpVCURTS6XR1yKgdHZ1iMYdaKVtdf0ZB4uGUKmM9Jj3Q0clI088RoPp6lf19gwlSlhW6q3xhum7wcZnvsVQqGdqsrLKzk2F+Ps6Vy5fp6enD5fJQKpeq1zFMK5P5RBAMwos3idPc92+dgMDZCMlpnfHj1nDSc3wTx7/2tYqi0N/fT3d3N+l0mufPn7O9vU0qlWJ8fJzW1laiUYOxEV2iXK5gt8sIggK6dlhigoSxHcSaIEa9+SVJkhF90jWrAapQMJqw1tZWGRm5TFd3FL3K2mL5ORiRNYfDRTq9SXxhiWw2R1dXD83BFkCsagoBdKnaC2Lyh53NmLmT3v9vnYCcNcfESW5co5lymtd+neMbo26NLa5mFjwQCHDv3j36+voYGxvjwYMH/N3f/R337t3j5s2bdHV1YbM5qtW6AppmZLINJ9xoTkI3eLOMy72qRTSqY+p0DbFKJSpJUnUSbwsupwNNVy2HXuCQW0zXIbm+SSKxRqS9E4/HhyQZnGCKbMydr3BYPKko0itreBM4zed0Lrh5zwqvC/Med+w3fbKfdc6k8Vq1xYxmBMrs/+7s7MTtdpNKpZiammJxcRGHw1HXqGVGl+r9Dx04OsReey1dN5xqWZbx+XwEggFj+i46siSjVg6Jq3V0FuOLPHs2xuLiEg6Hg1wuh6oatEaSJFu0QpJ0+AA4i4LF03xOQqVSeWW3nEVX25tC3YfzFTjuBh81+/A0AnLcGs7qvjVmoKF+vbVOsOmfmFn21dVVpqenWVxcJJPJ4HK5iEaj9PT00N7ebhVBWiaUKCKIBrHcURrkuPteu0ZZklFsSg3HlsT+fpY//OFTlpdWkSSFtrY29vf3q7REQYv21Ov11iU+zwKn+Zy+sxrkqzLpRx3/bdUgtX+v3cSyLOP3++nu7qa9vR1JkhgfHyeRSJDNZq2Mvcm5awiIUM1kGz5I7XUbBwbV1nXZqzVYmGX5gjkiAtRKhZXECmNjzwkEm7l75x6xWAxVVUkkEsTjcbLZLHBIXdRIHPFVAnOa+34qDaKq6itXPs8Ccpryk9Nk0k/znt+FBnmdUNeux5xbAjX9FzXjrff39/njH//IF198QSqVYmBggB//+Mf09/fj8/mq51WNsGulZJWnHA74rC9N0XUjP6IoitXsZF7TJLne39/nk08+YW93n6tXr/P++3cQRZFKpcLCwgIvXrxgZmaGYrFILBazhqqagmJqxqOExjThjiINPw6nEhCtcdAe578f5DR1VCc9x2kjWG9TQMxr1uIkgn/UMaqqsrOzw8rKCnNzc0xOTpLL5YjFYly7do3h4WG8XheCqKOqRsEi1Q1VywpZe00zl1K3Poxarr3dPaZnpvn444+5c+dDro2+R1tbxFproVBgd3eXzc1N5ubm2NzcRNd1i+iiv7/fYoApl8tWMab5YIBXSfa+Cqdy0o8jrz7PaFzvUV+nPcebXNdZ4CTrPck9EUURt9tNIBAgGAzi8XioVCpsb2+zurrK1tYmoCNKVJ3leiE4ab+8GcVaWVmpzoJXuXnzNpFIJ5J4OEFYURScTqfFTGmz2SiVSmxvb7OxsVF3TtMcrGXgNwMTR5HXfd29UYsL0oY3iPP6gDE3uEmgDYbJ5Pf7rbHX5rSo+fl5stkMpXIRBLDZ7CiKUp37fpgoPEmwJLWdYnpmmkQiwejoKH19A7hdnlfWZppJJl+Y2+1G0zRSqRSlUomDgwODDkiWsVfXU8vldVz2/03gQkDeIM6rgGiaRqFQIJ/P17HOmxy8gUCAoaEhenp6KBQKfP7gPvPzs+RyOQKBIK2trVAtIjTPVyscr5hXVe3x9OmXzM/N4fX5+MXPf4HD4YBqpW4jTC0gScZQ0Gg0SjjcQrlcZmlpiampaXZ2tvH5fdZQVV3TUTXNqlA+C5xaQE7jIJ8FThv+O4t11Kr2b6rC3wZM08g0UUzUPnnNiuHu7m7eu/Ee5XKRsbHn3L9/H01TcTod1tx4UzjM2i6D4E20vnQdsnv7PHr0CFVTuXnzJu2RCKIkIQpStZT98H41Di4ypw/7fG5aWkJ4vR5UtczG5gbJ9STlcgkBnURimSdPHlOplKvhYcViewTqomy1OE6wzc+0FqfKpJ82gnRWOA9rOOrc51E44FBAjqI0rT3G6XTicjkJhYJIokBTUxNTU1O8ePGC9fV1hoaGGLk0QmtbBF1XKZdKaLqOIBij4MxzFktllhOrCMhEIt1Eo31IolEKf8i3++oagRoB1lFsMk02P5IUxW6X8XidrK9vMDc3xerqEqWi4asIgobP56Gjo/uV91abCDVxlCAct6dOrEFOk6BrXNBZ4F0LybdBc9Sido1Hrbf+iS7Q3Bwk0hGhJRxif/+Ara0t0uk0uXwOURBRbDZkRUKSFERBplLRDEFRNXa20zx//gKXy81A/yDdXdHqaAPpyPvWuC7j3zqaVkYSRRwOGz6fB5/fh02R2T/IsrGxTjqzQ7lcMqJsCNhs9le4hk0fpfZ91qJxXzf+/cx8kPPAafRt2LjnExqlUgFZMWYjvvfee3h9XlZWEjx8+JDZ2RlcLic+rw+ny4WmGo1YiqKwv3/A3NwcL1++ZGhoiIGBAZxO56k/B0HQkUQBBB0BHUlW8Pv8tLe34/V6UTWV3d1dFEWhUCiQTu+yt5clHA5bIyYahcP8Xa12MYe3HvegO9fFihd4d1AUpTrL0ChjGRocJBwKMT8/z+eff85/+2//jZ6eHu7e+ZBr127g8zWRz+ctArxAIEAoFKqWvtewKp5CUHRA06pM8qoGAuTzebL7WXZ3d1lfX0cURWTZhsNeolLRsdufcuXKFVpaWupyI7VTs0y/x3itTKFQQNcP50vW4sQj2E5rYp1VVOFN1GJ9nWt+vzSRiqZX0LRK3dNVVVWy2X0SyyvMzc+wublJIV/CZnPS0tKGqqrs7e1RKpW4e/cuvb29eL1eayMe5Q8cDw1dr6BTHcumGW3C5VKZTCbD6poRktY0jWKhRLFojK0WRZFoNEpfX59VrGlG7FRVpVQq8fDhQ3K5HOFw2KogMJOgjfv2xJn0N+WDnOoJcsS13kSpyWmv3xix+qrjv/1Q0fUKmn5YjWv2pBsQyWTSzM3PMTk5TXzBYH0vl8uEw2Fu3LjBvXv3rIiX+aCqtfO/OvOtoellDD1ikDyYG91sP85kMlRUlYODHAf7eXIHBTK7u9hsNqsPxuDYOiyzmZqa4v79+xSLRcLhMF1dXXR2dtLW1kZTU9OrGuSk1bynFZCjcFqH1qzleVcwPxBN06wo0OuefkdVCX8rIajAq9W8tRAF40m7t5dldjbOF18YBAzhcJgPPviAaDSK1+u1/IFKpWKZWcArUbVXoaFqZYyy+0NGRmsYT43AajqoFZ1ySSVXHX1XLBax2Wx0dnYiCAKFQoHFxUX+5//8n9bce0EQ2NjYwO/3c+XKFS5fvkxHR0f9rbgQkONxISBf9V6EarUu7O8f8Pz5C54+fcrS0hK9vb3cu3ePoaEhaw5JbU/81xGQ42E2etWPtQNjL5dKJb788ks+//xz8vk8P//5z4lGoxbB3v3799na2mJoaIhf//rXdWe+cNIv8I0gVAfuOJ0uRkZGCAaDVm/8H/7wB6anpxkdHaW/v984/hT1XCeF8eDW0LVX2xw0TWNiYoLPP/+cly9f0tXVZQ0VNeu/7HY7yWQSt9v9yrkvBOQCDajvRf+qY/Vq/7lJwu31emlubiYUCjE9PU0ymWR3d9fiv2ppabGmab1Z1Cc9wSCKWF5e5vnz55RKJQYHBxFFkenpaSqVCj09MUKhELFYjObm5iO1/4WAfKtxms18BlfXq3xZgCIbvoZZSxUOh+nu7ubJkyc8fvyYnZ0dstks5XKZSCRiMUEa5zk6SWdAgCMy73VHVBOFek3Ze7FYJJVK8fDhQzY3N7l06RJXrlxhfHycyclJUttb7OykuHr1Ki0trbjdriPN51O13L6JqNJxvzvqbxc+yGtXB4Jpn7/pa57snLoOqqpRKqooit1qlS2VSpRKJZxOJ6WSQX4dj8d58OABoihy7do1fvKTn1iaxLxvFts8BquJ8fmf7L1pmjFTUVEUq1Px0aNHjI2N8eMf/5jr16/T0tKCqqrMzk7yb5/+G/Pzc8RiMX7x81/Q1dWF0+nGYHc5xDfqST9rx/1CQF67uqoz/fX5i1977pMcpUO5rFLIl/B4vEiSXP29buVPKpUKxWKRcrnM6uoqT58+5cWLF5RKJX7+859z48YNIpFIXdFkbd7JuJ+vX4/RSalasx4PDg4YHx/nyy+/pKWlhRs3bhAOh60ymkqlxMbGGqnUFopiIxaL4fP5UBQ7jUbVNzKxasN2F3iXeDefgSBQ7We3sbWVYm9vj0qlgtvtpqOjw9IITqcTn8+Hw+FgcXGRYrFoZd0PDg6IRqPEYjErZ2ESTxy22H71w9pM8pkZ8XA4zJUrV+js7KS1tRVRFCkWi8iyhMPhoKurm7a2NsqVMnabrTqE9MIHucAbhPHUNzb09PQ06XSaUqmEzWbDZjMIrU2zy/QLANrb2+np6SGbzbKwsMDi4iLJZJLR0VGLEf4o4objUDvrBAxG/FgsRkdHhzUKzmR2lCQZXdeskvqKWjYslWMe9N+oDuNCe3y/ISBSLBRZXl5ibGwMVVWx2WxMTU0xNjbG7u5unem8uLjI1tYWoVCIn//85/zVX/0VP/rRj6hUKvz93/89f//3f8/09DSapuF0Ok/dZ15LLGH2ldRm8A95t8zRChqiICBVebuOGrchH+m5v8ZB/6b+xnHnPwrvuiK4sbDtbdRjHeWPHefnCdVJM2Z/hc7xn1F9qQjW8af5PGszeh1mEQAACJ1JREFU2bquo2oq6UyaiYlxYrEow8OXcDgc2O12nj17ZhUr2mw2KpUKMzMzlMtlhoaGLCKG0dFRIpEIS0tLPHr0iH/5l3/hyZMnXL9+ndHR0erMEMN0KpfLlillcQTX+Cq1dWPmvaxNGJr/FiUjb2KaVJquIagGYV7jjpNPWxv1TbXGaTLp56FAsLGp6G1c76TNPMZhh62wtSa03mhPC0esXz/m2GMXx6EwVjsKM+k0U1NT3L37IU1NTTidTsLhMJlMht3dXcrlMoqikMlkyGazln8iyzLlchmPx2ORSLhcLpaWltjZ2eHFixdsbW3R399PZ2enNUnLfA+VSsXqsT+KjqjxZ+NhW8v4YrwhncPx2kd9vhc+yGtwHgQUjg6GHAqH/trj3tgazP9qrqFpGrlcjmQyyfb2NktLBqVoJpOxQr2VSoVyuUwikUAQjLEN4XC47olvEkjcvn2bvr4+FhYWmJqaYmVlhf39fdbX1+no6KCzs7NuklbtUJ7aEPGR6xfMfIpevXnGz/UV3xcCcoE3CPP5US5XmJ6etmary7JMLpejXDYc4GKxyMzMDHa7nfb2dgKBwCshcbNWKxgM0tzczMjICLOzs9akX7/fzy9+8QtrkpYoila1cG0e5evgMFH56t8uBOQC3wiCYMw87+/vZ3BwELfbTTKZZGVlxTJdCoUCa/9/e9fS2zQQhD87dew8TJIScPpIeVSBqgUJhBAXbhz4pdy5IHFDSFw4RMoFqIIoBAmKwqMthCSuXxzSWdbbteO0BQTsJwUJd73rnd3ZnZmdmX3/Hq1WizEH5dniw2LDMGTphQzDYPcv9no9vHjxAg8ePMCTJ09w5coVXLt2DYuLizEx61fgRBjkb9IpfiWyeh9Me2e2csLEOMipqwl6xUR3yFY24QsAAFGkHVhENej6HEolG8vLTVSrVTQaDVQqFYRhiHK5DNM0WRzGYDBArVZjieqoT6LhhtcnSCQrFoss02Kv18PW1hbzviVv4cm38fpGXGeOt6MfdIfXVYDhcITdnT6Wl5fZ82MzyKxBSYpJ4mWPziD8wZaon0SHz7xkbj6Sd5PAzrPZP5P8VpVqDWtra5PIvoMDwL29Pdi2zdzcd3Z2EEURbNuOZZMX+8+fZ/An6lTXysoKHMdBt9vF9vY2MyWfO3eOxarzOpJo2Yq3J9BDizAeu/jw4cOfZZB/GbNEG8aVw6PWmzTppX9KqDtbOcTcijTWRLVSw8bGBjqdDt69e4dcLodutwvHcVCv1+H7Pj5+/IhCoYBCocDuJZEtGrwbvKZpTMeYND/J23X16lVcuHABW1tbePz4MR49eoTz58/j+vXraLVaLHcXmXTJTYjqnNBS4m4fRYhCjYl4BKWDKBwLlmVhZWUFnz59wps3bw6yMdZw8+ZNNBoN9Ho9fP78GWfOnEGxWExkDhnEcuQIqes6Ll68iKWlJbx69QpPnz7F/fv34TgO7t69i2azGTs/yQrTNFGv12PPFIMoHBtzc3NYW1vD0tISfN+HZVmo1+ssY8hoNMLi4iJM0zyWKZo351LQ0yQbvY1ut4vNzU3cu3cP6+vruHHjBi5dujRTcFahUMDCwkK8b1lfTnNVV5gNfyPdkiY2yfmULZ4QBAE8z4PruoiiCPPz8zGR6agQM7ufOnUKxWIR1WoVpVIJ7XYb/X4f7Xab3X8iS8YgA/lnxZ7JCpJiEwTBwaXvdJVWPIt22kDLdJNZmUwmo6cpvLL/Z32eNnCyd6Yp42llpzGITF85Ck46XdG08aPzCJo7+/v7CIIApmmiVqsdmnxZ20gqw5uIG40GHMfB+vo6Op0Onj9/jpcvX2IwGGB1dRWO46BcLsdO48U6M0cUko36y5cv2NzcxOvXr2EYBkzTZF6WZHuWyZSapjFlLNYY955YXvzoXG7iliy6EPi+f+iQiWI1RCWPblcVCUtObDIiySD6Y1HdIkgp5JMxi56mWXBSk/okmUM0oRKSbnci8cowDJw+fRpnz55FPp8/0fMK2RgsLCxgfn4ely9fRqfTwcOHD2HbNm7duoXbt2+z0Nqsi7U0cRxln9je3ka73cazZ89gGAbrYBAEzBcmCbIVlNI8yrwmRVA8AG3V5Lbgum7smjEgfq+duIqLndZ1naWjEZlPJAWd1uq6zsQFsnKQEiijm6b99CTlxQEevKuE2KZsx5H1g9zCRfcPWqAKhQJ838dwOGRxEll2Lz4dp2EYjAaysSMaiQiCAKPRCP1+H7u7u2i1WrAs69ACSYtHLpeD7/uxn2zn9jyPLZLUbxKN6B4TOnAcDofY29vD27dv4Xkems0m7ty5g42NDVQqlVQ6EKQ7CA2IbdtYXV1FqVRiE5YISL8kbpRtV/SObGLIxBMy1fGTk08dw5fnPTz5OpPMiVm+mfccdV0X4/EYrusiDMNDDMZ/L71HVhQSNfh2xDQ4/HMZfURm1nUdlmUhn8/HGIR2fwp39X0f3759QxiGrGwSkmLDqV80cUUayerlzx2KxSIGgwG+f/8urZ92Z1oI9/f3meeuWJ5nEP59knD4+ZXL5VAul1Gv1/H161e22PKi4DRIdxDRbZgnnqziWQ7Hpv1NVla84ljmvSljBtnzKJrciycOdBJo8tGuSUwq2z1pcHgG8X0f4/E4Zl9PYxDaIWV0EL+L/J5kO0g+n4dlWWwlD8Mw0w4C/BSFiSk8z2M/GYPIFhza3Xi3dJl4zNOYb4vGWqyXFhCRbrSA005H48PHgJRKJXajVtaE2lIG8TyPdZo6x2fCFldPmVwpm0CHTzOnx5lk6UTSu7PuIGl1ZynPr0x/OpblOEgyNvwLmGU8gQQGkVVyEjvI7yR2FqvUr2rzX5tU/zMyZ3dXUPgf8ffKAQoKvwGKQRQUUqAYREEhBYpBFBRSoBhEQSEFikEUFFKgGERBIQWKQRQUUqAYREEhBYpBFBRS8ANhXQTyD3adNgAAAABJRU5ErkJggg==)
physics-General
physics-
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
physics-General
chemistry-
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
chemistry-General
physics-
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
physics-General
physics-
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
physics-General
physics-
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPAAAAC/CAYAAADAW1ErAAAgAElEQVR4nO3deXRT54H38a92yZItW17lBeMF75jdBpxQcEgCAdKSKUyavZ02mWRmkumS00ybZpq2MyfTzEw656TzR3NKSUhDswOBkBACJCxO2DdjFmMDxvsm2dqXe+cPXt03rknCLst+PufoHCNfSc+1+fm591lVsizLCIIQk9TRLoAgCFdOBFgQYpg22gW4VlwuF06nE41Gg9VqxWQyEQgEcLvdmM1m9Hp9tIsoCNfcqAnwvn37eOedd4iLi2Pp0qVUVVXR2trK9u3bmTlzJkVFRdEuoiBcc6PmErqkpIRZs2bR0NDAoUOHlOc9Hg/19fWItjphNBo1AU5JSWH+/PmYTCb6+/sBsFqtTJ06lalTp6JSqaJcQkG49kZNgDUaDTabDZ1ORzgcBiAUChEKhbDb7VEunSBcH6PmHhhArVajUqlwuVycPXsWt9tNenq6aMASRq1RUwNHpKSkANDS0oLb7SYzMzPKJRKE62fUBTg9PR1JkvB4PKSlpWEymaJdJEG4bkbVJTRcaLgKBoMkJyeTm5sb7eIIwnUV8wGWZZmenh4SExNxuVykp6dTUVHBxIkTo100QbjuYj7Afr+fl19+mTvuuIPjx49TVFREcXExOp0u2kUThOtOFeuzkRwOB7m5ucyaNYsnnniCmpoaEhISol0sQbghYj7AoVCIuro68vLySE5OxmAwoFaPurY5QbiomA+wLMv4/X4MBoMYbSWMOTEfYEEYy8S1piDEMBFgQYhhIsCCEMNGXYAlSUKSpGgXQxBuiFEV4GAwSGdnJ06nM9pFEYQbYlQF+NSpU/zP//wPmzZtinZRBOGGGFUBDgaD+Hw+ZUK/IIx2oyrAoktbGGtGVYAFYawRARaEGCYCLAgxTARYEGKYCLAgxDARYEGIYSLAghDDRIAFIYaJAAtCDBMBHgPcbjcNDQ309/d/6Wg1SZJwOp0cO3ZMjGiLITG/rKzw5fx+PwcOHODNN9+kv7+fn/70pyQkJKDRaIYc5/V62bt3L6+99hq5ubkUFRWh1Yr/GrFA1MCjWDAYxOVyce7cOTZv3ozH47lo7RoKhejo6KCuro6GhgZRA8cQ8Wd2FNPpdFRUVLBkyRI+//zzLz3OYDCQm5tLdXU1Pp8PuLDedm9vL8FgkLS0NGw2G7Is4/F46OjoIBgMKq9PSEjAZrNhNBqv+zkJQ4kAj2IGg4GMjAzGjRv3lcfp9XrS09PJz8/n2LFjwIW51du3b0eWZWpra0lKSqK7u5uDBw/S2NiIx+OhtbWVpKQkZsyYwbRp00SAL4HX62VwcBCA+Pj4q958T1xCC0PIsozL5eLEiROcOnUKSZIwGAz4/X727NnDiy++iNvtRpIkXnvtNerr6wmHw+Ke+RJ1dnbyySefsHnzZs6ePXvV7yd+6sIQfr+fjRs3sm3bNh577DEqKyvRarV0dXXR2dmJ3W7nySefRJZlPvvsMyoqKigrK8Nms0W76DHBaDTicDg4c+YMycnJlJSUXNX7iQALilAoREtLC4888givv/76kNZonU6HWq3G4XAoxyclJYma9zKlp6dTXFystDVcLfHTFxQajYaMjAzmzZvH6tWrGT9+PGVlZcCFhqpJkyZx/Phxnn32Wex2O5s2bWLRokWkpaVFueSxQ6VSodFortn+XeIeWFCoVCrMZjN/93d/h9fr5YMPPlDu02RZJhQKoVarKSgowOv18txzzzF79mzi4uKiXPKv19/fz5o1a1iwYAELFizgpZdeoru7O9rFumqiBh7F/H4/586d47PPPsPr9fLJJ59gsVjIzc1Fr9crx7lcLk6ePMmePXs4ceIEvb291NTU8OGHHyLLMosXL8ZqtdLU1MSpU6coKytDq9VisVjo7OzEYrFgsViieKZfLRAIcP78eZqamliyZAlOp5NXX30VjUbDokWLSE9Pvy6f6/V6OX78OA6HA1mWmTZtGlar9Zp+hgjwKBYMBunp6cHtdjNnzhwcDgc9PT1kZ2cPOc7n8+F2u0lMTKSoqIjz588zadIkTpw4QV9fHx0dHSQkJGCxWDAajcq62+fPn+fs2bPIskxJScmI7UZyuVz4/X5mzZrF1KlTcblcHD16lN27dzNlypTrFuBAIMDZs2dpa2tDlmVKS0tFgIVLp9PpyMjIoLa2ltraWlQqFRkZGcManoxGI8XFxVitVtRqNVarFavVykMPPYTX68VutxMKhbBYLMNqrPr6enp7e/F4PCM2wGq1GrvdTlZWFnChf3zevHns3LkTt9s95FhZlvH5fDQ3N9PX10d6ejrHjh3D5/NRUVFBWloaDQ0NNDc3M2HCBKqqqtBqtbjdburq6pSfl81mw263k5ubS2JiIrIsExcXh9/vp7e3l7a2NiwWC06n86pCLQI8ihkMBvLy8sjLy/vK4ywWC6WlpZSWlg55/ouvq6urY+/evVRUVDBu3Di0Wi0+nw+/309SUtKw8dUjSWJiIomJiUOe02q1pKWlDRtIEQqFOHfuHC+++CIOh4PFixezc+dODh8+TG1tLd/4xjfYvXs3H374IVarlZdeeonk5GSOHDnCunXrlD8WycnJfP/732fKlClD3r+/v5++vj66urqIj4+no6NDBFi4/tRqNc3NzezYsYNZs2ZhNptxuVxYrVZKSkqu+aXh9SRJEgMDA9TU1JCTkzPke6FQiPb2dtatW0deXh42m41nn32W3//+9xw+fJiioiK++93vUlVVxZ133smZM2dISEhg06ZNVFdXU1tby6FDhzh+/PhFP1uj0VBUVITRaCQxMRGDwXBV5yICLFyS6upqCgsLOXDggNIyPW/ePAoKCq76P+GNJEkS/f399Pb2snjx4mFdYCaTiWnTpvHUU0+xY8cOJkyYQEpKCna7HafTSUZGBunp6crUzMgEEYPBQH19PSkpKUybNo3a2tqLfn5CQgKzZ89m9uzZ1+R8RICFS2az2Zg3b54yW0mtVl+z/swbxefzsXLlSu6+++5hjXlX4+677+a3v/0t3/3ud5kwYQJPPPEEd9111zV7/y8TWz99IaoigxC0Wi1arTbmwuvxeDh69Chz585l/PjxQ7rSrlZWVhb/+q//yurVqykvL+cPf/gDe/bsuWbv/2W+tgb2eDy4XC4x2kaIaQMDAzQ3Nyv94CaTifr6enQ6HZmZmcTHxyvHyrKM2+3G6XQSCoWAC326AwMD+P1+JEnC7/crz0uSxJo1a0hKSqKkpES5fPZ4PNf9vL42wPv37+edd97hRz/60TW95BCEG6Wnp4dNmzaxatUqTCYTFosFlUpFKBTie9/73pDWdqfTyUcffcTrr79OR0cHK1euxG638+GHH3Ly5ElUKhW9vb28/vrrBAIBnn/+eaxWK52dnXi9Xg4cOMDBgwcpLCwkPz//up/b1wa4tbWVTz/9lMcff/y6F0YQrgedTkd2djZz5swZ8nxCQsKwUWlarRa73c6yZcsAyM3NxWg0smTJEhwOB5mZmWRkZFBTU0NNTQ1wYVJHTU0NGo2G06dPYzabqaysJCMj47qf2yU1Yul0OpKTk693WYQbwOPx4PP58Pl8SJKETqfDZDJhNBqv6T3hSGK1WpkzZ86wAF+M2WweEs4vc+utt170+YkTJ15RGa+U1uFwoFKplK6AQCCg/GINBgNJSUmUlZUNuUcQrr2TJ08qU/WSkpKw2Wx0d3czMDAAQGFhIVar9YoGTEiShM/no7OzE6fTidvtxuVyEQqFMBqNmM1m4uPjsdlspKSkoNPprum5CdePdv369eh0OqZNmwZcGBo3ODhIbm4upaWlTJw4kYSEhCgXc/TbtGkTO3bswOFwUFVVxYIFC/jwww/ZuXMnmZmZPPHEE5SXl192gEOhEAMDA7S2tnLo0CE0Gg1GoxGtVks4HGZwcJBz584RDoexWq1MmzaN9PR04uLiUKlU1+lshWtF+0//9E/Isswf/vAHDAYDv/zlLzl79iwPPPAAjz76KMXFxdjt9miXc9S75ZZb6Ozs5O233yYxMZGFCxei1+tpbGxk+fLlZGdnX3bNGA6H6erq4ujRowwMDFBdXU1iYiLhcJhQKKRMYhgcHMThcNDX18fmzZspKytj8uTJmM1mEeIRTvPKK6/88t1338Vut2O329Hr9fzkJz/hwQcfJDMzM6Z+gR0dHRw8eJCsrKwbfi9ytVJSUpg5cyYGg4G6ujp27NhBXFwcr7/+OjNnzsRisVx2v2t7ezvHjx9Hq9Uyd+5cUlJSMBgM6PV6dDqd0p8b6dvV6XTIskxzczNarZakpKRRe188Wmjnz5/PK6+8wg9+8AO2bt3KCy+8wIwZMzAajTEV3linUqkwmUwsXbqUnp4eXnrpJcrKyrBarVf0e/B6vbS1tSFJEtOmTcNkMqFSqVCr1UPeT5ZlwuGw8giFQgQCAY4dO0Z6erpyuS2MTFqz2UxhYSHx8fGcOHGChoYGysrKhs3S8Pl87N69m+bmZsLhcJSK+9VaWlqor69XWlpHovj4eIqLi6msrBz2PZVKxcmTJ5W5qx999BErVqzgwQcfvOwQRSbm5+fnK/2eEWq1Go1GQzgcRqPRKA2WwWBQmfLW19fHwYMHMRgMZGZmXvV5xwqfz0dDQwOvvvoqM2fOpKSkhPz8fMxmc7SLdlHa9vZ2NmzYwNNPP01TUxPr1q1Dq9WyePHiIfM+IwueRRo8RqKOjg4GBwfp7e3l3Llz0S7ORcXHx5OUlHTR733++ec0NjZSVVXFHXfcwcaNG/n973+PRqPhb/7mby65J8Dn89HX14darVZWi7zYbguRGlmj0Qy5jNbr9RgMBqUVPCMjI+aGTV6pyM9h48aNfPrpp6Snp2O1WsnJyaGiooJJkyaRl5c3YlYg0b7xxhsEAgHl0u3Xv/41b775Jn6/n0WLFpGVlYVWq0Wv1zNp0iTy8/NH7NYbp06doq+vj7KyMm677bZoF+eidDodKSkpw57fvXs3K1asAODee++ltLSUxsZGjhw5wosvvkhHRwf333+/Min9q0S6iCIrSUb+4EZqYUmSkGVZeUREJidEghwOh2loaKCzs3PMBFiWZXp7e7HZbBw8eJAjR44gSRKJiYnk5+dTUFCA3W4nJSWFnJwcSkpKKC4ujlqDn3bnzp1Mnz6dpKQkZFkmLy+PU6dO8cknn2C320lMTMRqtaLX66moqLjhBbwccXFxHDhwgKKioms2XetGGRwcxGq1YrFYlC6clJQUZURQf38/gUDgkt7L6XQSDAaVy+LIeN5ICCVJIhwOK0H+YqC/WCur1WoOHDhAW1sbLpfr+pz4CBQKhQgGg2g0GmWsc3d3N319fRw4cACNRkN8fDzZ2dmUl5cr62dHY3E/bU1NjXJ9L0kSBQUFfPvb3wYu1BaSJN3wQo1FU6ZMobCwEJVKRUJCAmazmaqqqiELf1/q0Dyfz0coFCIcDuP3+9Hr9ciyrDRgRQIceUiSNOwRodFolEvqsUKlUjEwMEAoFFJ+bmq1WvnaZrORmZlJYmIifr8fl8sVtdtK7ZNPPqn8Iy0tjYceeigqBRnrbDbbsN0NUlJSLnq5/XUiYfN6vXg8HrRaLZIkKYNAIrVtpKaJhD0S5khrtCzL3HTTTUyaNOmKyhGLJEmipaWFxx9/nJaWFsxmMzabjeTkZEwmE4mJiZSXlzN79mwqKirIz8+P6u2F6B8YhRISEtBqtXi9XtxuNxqNRhkeG6mBI91HwWCQQCBAMBhUvo4EGVBWohwrfD4fp0+fZvfu3aSmplJRUcHs2bOprq5WFrUbSUSARyGr1YrRaKSvr4+BgQGlBo4M2gCGBTjy8Pv9+P1+ZUy8xWK56h30YonRaGTGjBl88MEHlJeXj/g+8JFdOuGK6PV6rFYr7e3t9PT0oFarMZvN6PX6IWOpJUlSLqP9fj8+n08Jsc/nIzk5mYSEhBG94uS1plarsVgsyuL1I93IL6Fw2VQqFYWFhbjdbpqamtBqtcrMI61Wi0qlUu6Dw+GwUvv6fD48Hg9erxe4MDUuNTU1ymdz46lUqpiZkSUCPEolJCSQl5eHy+Wio6NDWZg9MmgDhl9GRyY3hEIhJk6cSFZW1phqfY5FIsCjlFqtJi0tjdLSUlQqFe3t7fh8PvR6vbIgXaTLKDL+2e/3o1arqaiooLS0dNgQTGHkEQEexYxGI9nZ2ej1ekwmE+3t7QwMDCj9ml8cwKFWq0lOTmbcuHEUFRURHx8/ZkZfxTIR4FFOr9eTlZVFUlISp06doqurS2m0inQt6fV6zGYzWVlZ5OXlieDGEBHgMSCy7+/kyZMBcLvdDAwMEA6HMZlMxMfHi3m/MUoEeAwym80jdnqccHnEtZIgxDARYEGIYSLAghDDRIAFIYaJAAtCDBMBFoQYJgIsCDFMBFgQYpgIsCDEMBFgQYhhIsCCEMNEgAUhhonJDGNIOBxm7dq1vPXWW/T397NkyRLuvPNOsrOzhx3rdDrZunUrwWCQqVOnUlBQEIUSC19HBHiM8Pv91NfX09fXR21tLU1NTWzduhVJkvjOd75DcnLykOMPHDjAn/70J/Ly8igsLIxSqYWvIwI8RoTDYXp6epg+fTolJSX09PTwm9/8hvr6elpaWoYF2GazKbsRCCOXCPAYodVqGT9+PAUFBWg0GrKzsykqKqK5uZn+/v5hx1dWVg7ZC6ulpYUDBw7gdDoZP348N998MwAnT57kyJEjQ94jNTWVOXPmfOkujMK1IwI8Ruj1eoqKioY8p9VqsVqtJCQkfOVrA4EAe/bsYcWKFahUKubPn8/NN99MZ2cnGzZsYNeuXXR0dHD27Fn8fj/f/OY3mTx5sgjwDSACPEZF9kTKzc0dFuy/Pq65uZnBwUFuu+02li1bht1uB+DTTz/l9OnT/PCHPyQ9PZ0XXniBlpYWnn76acaNG3ejTmVME91IY5Asy7S2tpKVlUVFRcVXbhze1tbGn//8Zzo7O7nvvvuU8MKFfYQKCwtJTU0lLy+PrKwsZUdE4cYQAR6DfD4fmzdvJjc3l6qqqq88Ni4uju7ubhoaGnA4HEO+N3HiRDZv3szJkyfp6Oigr68Po9E4bJdF4foRAR6D6urqlN32vm7fI5vNxrJly7Barfzxj3/E5/Mp3ystLeX222/n+eefZ86cOZw/f56///u/JzEx8XqfgvD/iHvgMUSSJLZv305WVhZZWVmYzWaOHDmCx+Ohurp62PEulwuAyZMnk5WVxccff8xbb73FfffdB8Du3bsxGAw88cQTJCQkkJaWxvjx48fUZmjRJgI8RgwODrJu3TpWrlxJUlISRqMRtVpNQkICtbW1w45/5ZVX2LlzJ4ODg1gsFlJSUmhpaeG///u/2bdvHy+88AKBQIAPPvgAlUql3EdnZmZy6623Mm/evBt9imOSCPAYodFoSEtLY/78+YRCIeX5nJwcSkpKhh2flpbGd77zHTweD8XFxSQnJ2O1WmltbVW6nUwmE1VVVfj9fmUrTkmSOHPmzI05KUEEeKyIi4vj1ltv5dZbb72k4xcsWMCCBQu+9PuyLLNp0yZqa2uZMmUK8fHx+P1+9u/fz4kTJ65VsYWvMaoCrFarxW56N9D27dsJhUK0tbURFxeHVqslEAiMyT2Fo2VUBTg+Pp7MzEysVmu0izLqqVQq/vmf/5k1a9awbds2vF4vFRUVLF++nPnz50e7eGOGSh5lo9UHBgbQarXExcVFuyiCcN2NugALwlgyJgZy9Pf3c/fdd7Nz5048Hk+0iyMI18yor4EDgQD19fXU1taybds2ysrK0Ol00S5WVIXDYTo6OpThj5EBGxaLhdTUVGw2G5mZmUrXkDByjfrfUCgUwuv1cvvtt5Oenj6m/1PKsszAwACHDx9mcHBQeU6r1SJJEg6HA4fDgVqtJjU1lbKyMpKSksTIqhEs5mtgr9fLv/3bvxEIBPjbv/1bysvLCYfDyiTzmpoa9u7dSzgc5uabb8ZoNEa7yFERDAY5c+YMbW1tSJJEfHw8JpMJtfrCXVQgEGBgYIDBwUEGBwcJBAKkpaVRWFhIZmYmJpMpymcgXMyoqI4CgQDr1q0jLy+P7OxsTCYTZ8+e5dy5c8ydOxe73U5WVhZ6vT7aRY2KcDhMX18fDQ0NJCcnk5+fj9VqRaVSEQwGCQQC+Hw+TCYTFouFuLg4ent7aWtrw+/3o1arGTdunKiJR6CYD7DJZOK3v/0t4XAYj8fD4OAgycnJjB8/Hp1Oh8lkorS0NNrFjJrIZfPp06cxm81Mnz5d+UMmSRIajQaNRqMMgFGpVMiyjCRJAPT09HD69Gnl/lgYWWI+wBFTp07F4XAQDocJBoMkJydjNpujXayo8/l8tLW10dLSwm233aaEV6VSKYvWaTQatFoter2ecDiM0WgkLi6OQCCA3++npaWFuLg4rFbrmL2KGalGVTdSZJmY5uZmBgYGmDBhQrSLFHV9fX2cOXOGjIwM4uLikGX5osNNIzVx5GEwGJQgS5JEV1cXXV1dUTgD4auMqgAfOXKE8+fPEwwG0el0GAyGaBcp6jweD06nk+TkZEKhEJIkDXnA/79sjnytVqtRq9VKzazVavF6vRddvVKIrlET4LKyMuLj4zly5AgajeaiU+TGmnA4TCAQQJIk5fL4iw9JkoZ8HXnIsqzU1Gq1Gq1Wi8/nG7akjhB9o+YeWK/X09HRwZQpUxg3btyYH6wBF3Zj8Hq9wIXbi8hyOFqtVrn/jYQ4FAopQY4E+Iu1cjAYxOPx4PP5OHv2LG63G4CCggLi4+Pxer10dXXR39+PXq8nPT1dafRqaGjA6/Wi1WrJyMggLS0Nr9dLW1sbTqcTgPHjx2O1WgkGg7S3tyvvk5KSQkZGBgAnTpzA4/EgyzI5OTmkpqYqn9vb24tKpSI7OxubzYYkSZw/f57+/n50Oh3JyclkZmYSDodpamrC7XYjSRI5OTnYbDaCwSDd3d10d3crc6fT09NRq9WcPn0ap9OJRqMhOTmZ7OxsgsEgra2t9Pf3I8syWVlZ2Gy2G/7/btQE2OFwcOeddzJ9+nQsFku0izMiRC5/Q6EQPp9PGUaq1+uV++BIrRsJceTx17V1RGtrKy+99JLyh2HJkiXMnDmT06dPs2XLFs6cOYPZbGbSpEncc889tLS08Je//IXW1lYGBwdZtGgR3/72t2ltbWXVqlX09vYCMH/+fObOncv58+fZvHkzjY2NGI1GKioqePDBB3E6nbz88stK4CPHd3V1sXbtWs6ePYtGo6GqqoolS5bQ1dXFhg0bOHXqFFqtlsrKSh544AHcbjd//OMfcblcyLLM3LlzmTNnDg6Hg02bNnH8+HF0Oh3FxcU8+OCDOBwO1q1bR2NjIyqViqlTp7J8+XJ8Ph8vv/wy3d3dyLLMrFmzqK2tJTMz80b+imM3wD6fj5aWFo4fP05GRgaSJHHzzTcrfzUFlHYASZJwOp3KIJZwODykTzcS0kAgQCAQIBgMKg2CkTDr9XoSEhKwWq3cdNNNyqoe48aNQ6/Xk5qaytSpU8nLy0Ov1yvLz8bFxTFz5kzq6uo4duwY4XAYrVZLYmIi1dXVyh+CvLw8DAYDNpuNyZMnk5OTg1arJT09HZVKhV6vZ/bs2cpVRH5+Pnq9nsTERKZOnUp+fj5qtZrs7GylrJMnTyY7Oxu1Wk1iYiIdHR3o9XpmzZpFKBRClmXy8/OVQSqVlZXY7XalptVqtZhMJqZMmUJOTg4A2dnZyvMzZszA6/UiyzK5ublRmQEXsyOx+vr62LZtG2+88Qb33HMP5eXlZGdni4arv9LU1MSuXbswmUxkZWURHx+P0WhEq9UOqYVDoZAyqMPv9+PxePB4PLhcLgYGBkhISGDSpEkUFxdfUTnefPNNjhw5wje+8Q1uueWWS3qNJEl4PB7a29txu92kpaWRmpo67DI1HA4zMDDA2bNnsVgsyh+VyPcaGxv5/PPP6e/vx+VysXDhQioqKkZFl1jM1sCRbUHGjx9PcXGxuO/9EvHx8WRkZHD+/HmcTieyLBMKhdDpdMqVyhcvoSP3ypEg+/1+wuEw8fHxwzZAuxwdHR0YjcZLXnJWkiS6u7s5evQoHR0dtLa2Eg6HueWWWygrK1Nuk4LBIOfPn+fTTz+lv78flUrFjBkzmDhxIvHx8XR1dbFnzx4OHDhAUlISBw8e5PTp0zzzzDPk5OTE/OiymL3WTEhI4JZbbuG5556juLhYhPdLJCUlMWHCBLRaLX19fTgcDgYGBhgYGMDlcuF2u3G73Xi9XrxeLx6PR/k6ct/c09OjNCwFAoHLLkOk4ctqtSoNUl8nEAjQ0tLC4cOH0ev1mM1m/vKXv7B69Wra2tqU4zo6Onj//fdZv349SUlJ9PT08PLLL3P06FH8fj9Hjx6lv7+f+++/n5/97Gf8x3/8Bxs3buT06dOjYgeJmK2BhUuj1WpJTU2loqKCzz77TKmBDQbDRVujg8Egfr8fn8+H1+tFkiQaGxtZs2YNu3bt4rHHHiM3NxebzXbJ6481NjbS09PDnDlzyMrKuqTX+P1+MjMzefTRRzEajciyjNVqZdu2bUpDVigUYteuXaxfv55f/OIXzJ49G4Dly5ezdetW0tPT6enpob+/H4vFotxTR3ZWjPSDx7KYrYGFSxcXF8eECRPIzMzE4XAoNbHT6RwyA2lwcBCXy6Xc9wYCAYqLi3nmmWd47LHHqKur44477uDpp5/G5XINaZ3+MrIss2HDBkpKSigoKLjkMlutVjIzM4fMHsvLyyM/P19pLGptbeXQoUMEg0ElvABLly6lqamJ5uZmVCoVXq+Xnp6eIWO8R8vihyLAY0RkWdmamhpUKhW9vb10d3fT29uL0+nE6XTS399PX18fAwMDqNVqZs6cyfTp0xk3bhx33303a9as4Wc/+xnvv/8+5eXl/Od//iednZ1f+pmSJHHo0CGOHj1KdXU1hYWFV1R2WZZxu91s376dxYsXK6PygPoAAA1aSURBVO/T19dHMBgc1rCWlpamjMqbOnUqwWCQZ599lh07dvDJJ58gSRLFxcWjYqy8uIQeI1QqFSaTieLiYlJTU2lubqatrQ2Hw4Hb7UalUqHT6UhMTCQrK4v8/HySk5MxGAyo1WpMJhN5eXnce++9VFVV8fbbb7Nq1So2bNjA9773PRYuXEh6erryeeFwmM7OTn73u9+xdOlSKisrr6jV1+Fw8NFHH/Hqq6/S2dnJ9OnTlQBHRpj9dc9DSkoKKpWKcDhMbm4u9957L5s3b+aNN94gKyuLZ555htTU1FFRC4sAjzFGo5H09HQsFgv5+fkEAgHlUlij0aDT6TCbzVgslmEttFqtVtmhITU1lVtuuYXVq1ezcuVKNm/ezF133cWCBQtQq9XU19fzpz/9iTlz5jB79mwSExOvKDCSJOHz+VCpVJw6dYqnn36a5557TrmPValUw8r5xRZ2g8FAaWkpycnJdHV1YbFYKCgoGDWNniLAY5BGoyEhIUHZIuVyabVaCgoKKCgoIDk5mf379/PJJ5+wYsUKdu7cSWpqKm63m0mTJrFgwQJSU1OvuLvGbDYza9YssrKyKCkpYeXKlRw/fpwpU6Z86Wt6enqGtDAbjUbGjRs3KjcdFwEWrkqkz7WoqIiPP/6YAwcOsH79emw2G7/5zW+uKrxwoQYtLCxUHhs3bsTtdhMIBJTpkS0tLUNe09bWht1uHxP7FIsAC1fNaDQyb948Jk2axI4dO3j77bc5e/Ysf/7zn+ns7FRq0Ksd+ZSWlkZiYqKyu2JaWhrJycns3r2bjo4OpY+5vr6eiooKcnNzr8XpjWiaX/7yl7+MdiGE0SHSSHbTTTdhMpn47LPP2LhxI8FgEFmWMZvNQxbS+yqBQACn00lvb68y8GTv3r309PRw++23K91Jfr+fxsZGHA4HWVlZnDt3jrfeeotZs2Yxbdq0UdHS/FVidiy0MPIFAgH+/d//nffeew+A+++/nwULFpCZmfm199/d3d0cPnyY48ePAxfuu9evX8+Pf/xjqqqqlL5gh8PBxo0b+a//+i8efPBBDh06RG5uLvfddx95eXnX9wRHABFg4brr6+vjV7/6FWvWrCElJYWHH36YBx54QJnueDFut5sTJ06wZ88eNBoNmZmZzJw5k8TExGE1eCAQ4Ny5c2zZsgW73c7cuXOVDcdHOxFg4bqTZRmPx8Px48d56aWXWL9+PYWFhfzDP/wDy5Yt+9LXRCZYfHFlkC/rivrisTqdblT08V4KEWDhhvH7/fT09LB7927eeust9u7dS3FxMb/4xS+orKwUU0GvgAiwcMMNDAzQ3NzM/v37Wb16NW63m8mTJ/Pwww9TWlo6Kubp3igiwEJURBac//zzzzl06BAbN27EZrMxffp0Fi1axMSJE6NdxJggAixEVSTIGzZsoK6ujlOnTpGdnc28efOYOXPmZc1gGotEgIUR4+zZs6xfv55t27bh9XopLy9n7ty5VFdXj4lRVVdCBFgYcQ4fPsy7777Ltm3b0Gg0LF++nMmTJ1NeXk5cXNyYaWG+FCLAwogUDoc5dOgQ//u//0tdXR02m42nnnqK0tLSYRP9xzIRYGFECwQCHDt2jB/+8IccOXKEmpoannzySaZOnYrBYIj5RemulgiwMOKFw2F8Ph87d+7k2WefpampicWLF/Pwww8zY8aMaBcvqkSAhZgR2UZl7dq1vPPOO/T29rJw4UIeffTRMTHu+WJEgIWY09nZSXNzM5s2bWLr1q3o9Xpuvvlm/vEf/xGr1TqmGrlEgIWYJEkS586dY9++fXz++eds376dwsJCbr75ZpYvX37JC8jHOhFgIaYFAgHOnDnDxo0b2bdvH83NzcpGY9OnTyclJSXaRbyuRICFUcHv93Ps2DHefPNN9u7di9VqZcaMGcydO5fy8vJRO7FfBFgYdTZu3MiaNWs4evQoJSUl3HbbbVRWVipbzIwmIsDCqBQMBnnrrbd4/fXXaWlpYerUqfzgBz8gJyeHjIyMUdPQJQIsjGpOp5M1a9bwu9/9DqfTybe+9S1++tOfKtusxvpe0iLAwqgXDodpb2/n3Xff5de//jWSJPHUU09x//33D9lNIhaJAAtjQjgcxu1209rayooVK1i7di1Wq5XHH3+cRYsWxexsJxFgYUwJh8O0trZy8uRJVq1aRWNjI5mZmSxbtow777wz5iZJiAALY1IwGOTo0aMcPHiQzZs3097eTmVlJbfffjsLFy6MdvEumQiwMKa5XC727dvHtm3bOHLkCD6fj5qaGubPn8/kyZNH/CZoIsCCwIWF5D/77DPef/996uvryc3NZc6cOdTW1pKTk4Ner6e+vp7Ozk6mTJlCUlJStIsMiK1VBAG4sAticXEx1dXV6HQ6jh07xpYtW3C73fj9fuLi4vjggw945ZVXMBqN2O32ETG6S9TAgvBXJEnC5XLxwgsvsGXLFoLBIN/85jdpaWlh1apVjBs3jh//+Md861vfivrsJxFgQfgK58+f5/nnn2ft2rV0dnYSDAZRq9UUFRXx85//nMWLF2OxWKIWYnEJLQhfISEhgdraWjQaDU1NTTgcDoLBIP39/ezZs4fx48eTm5sbtV0lRA0sCF/hxIkT/OpXv2LLli04HA78fj+RyGi1WrKzs3nqqadYunQpaWlpN7x8ogYWhK+g0+nweDwEg0FcLhc+nw+9Xo8kSYTDYQYHB2lsbEStVpOVlXXDFxIQNbAgfAVJkujs7KS9vZ3u7m7a29s5efIku3fv5uDBg7jdbvR6PTk5Odx3330sX76c/Pz8K/qszs5ONmzYgF6vp6am5pLW+RpdkyMF4RpTq9XY7XbsdjtwYWG9trY25s2bx5kzZ+jt7aW5uZmjR48q+ztd6ZI+RqMRSZLYv38/48aNEwEWhGvNZDJRUFBAQUEBsizjdrtpamqioaGBpqYmMjIyrvi9rVYrkyZNoqGhAa/Xe0mvEQEWBC5cKgcCAfx+P0aj8ZJalVUqFRaLhcrKSiorK69JOSwWy2WtGiICLIx5wWCQtrY2Tp8+zeDgIEajkRkzZpCYmDjiJ/yLAAtjXk9PD2vWrOGjjz7CaDRy6NAh/uVf/oXly5djNpuvyyANSZLw+Xy43W5UKhVms/mKpjKKAAtjXnNzM5WVlTzyyCMMDg7y2muv8fDDDzNt2jTKysq+dkaSLMuXHXKn08mWLVt47bXXsFgsLFu2jFtvvfWyyy4CLIx5WVlZyLKMwWBAr9ezYMECfvSjH9Hd3U0wGBwW4MheTREtLS1kZWURHx+Py+XC6XSi0WiGNGj19PQQDocxGo1otVp0Op2ybrVWqyUnJ+eKVswUARbGvEgXkUqlQqVSYTQaUalUGAyGYffAra2tvPvuu7z33ns89thj7Nq1i61bt7Jw4UKqqqpoaWnh448/RqfT8ZOf/IRJkybR2trKM888Q3JyMrm5uZSVlVFeXk5mZiapqanAhQEjGo2GV199lbVr19LX10dKSgrTpk37yrKLAAtjnl6vV74OhUL4fD6qq6sZP378kO/BhUvfY8eOUV9fjyRJLF26FLvdznvvvUdSUhI1NTXodDp27tzJli1bKC8vZ/fu3dTU1FBcXIzT6USr1aJWq9HpdMNq95kzZ5KRkUFGRsYlrdMlAiwIX+ByuWhsbOSRRx4hJSVlWA2cnp7OxIkT2bBhA2lpaUyfPh2TycTq1avR6XRMnDgRg8FAc3MzHR0dyLKMy+Xi+PHjjB8/noKCAqxWKwkJCRf9/Jtuuonq6mq0Wi1xcXFfW96R3UYuCDeQx+Ph/PnzeDwe7rjjjov2BScnJ1NUVIRarVZaqCM1alxcHEajEY1Go9SsWq2WyZMn4/F4WLVqFStXruTEiRN82QjmpKQk0tLSsNlsl9QqLQIsCFzYJK2np4f+/n5KS0svWvteCY1GQ3FxMffccw+pqans2rWL999/n9OnT1+DUosACwLBYJD29nbOnTuH2WwmNzcXh8NBc3Mzfr9/yLGBQACXy4UkSQwMDOD3+3G5XIRCITweD263G6/Xi8vlwu12K5fkdrudn//853z/+98nFApx6tSpyypjZJWQvybugYUxTZZl2traqKuro7u7m9LSUurq6vB4PBw7doyHHnqIzMxM5fjOzk7q6+tRqVTs378fu93OwYMHCQQCnD59mqNHj9LS0kJjYyPBYJCGhgYOHjxIf38/JSUl9PX1kZ6eftk7QgQCAU6dOsWUKVOGPC8CLIxpfr+furo6Nm3ahMfjYefOncCFWUiPPfbYsFlFzc3NHD58mJkzZ7Jv3z5yc3PZv38/paWltLW1sXXrVgwGAwaDgaSkJHbs2EFRURF33XUXK1asoKuri4ULFzJjxozLKqcsy3g8nmHPi/nAwpgmyzKBQIBgMDisYSky6OKLo6yCweCQQRwGg4FAIDBklQ640B2lUqnQaDRoNBq0Wi1+vx9JktDr9Ze93nQgEODcuXMUFhYOeV4EWBBigCzLBIPBYf3SIsCCEMNEK7QgxDARYEGIYSLAghDDRIAFIYaJAAtCDBMBFoQYJgIsCDFMBFgQYtj/AXe6eqmCypx9AAAAAElFTkSuQmCC)
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,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)
physics-General
physics-
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
physics-General
physics-
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
physics-General
maths-
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
If
then descending order of ![a comma b comma c](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAPCAYAAACWV43jAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAWtJREFUeNpjYKAe+AbETAyDFKgA8SWGQQwCgHg5rS0BRU8jEL8E4l9AfAGI5YnUWw/E1VD9z4H4BxDvB2JJEuznAeIuIH4KtX8dEAsiK9gCxJOggiDHroKGDDEApPYuEJcj6e8jIVRBjjsHxK1AzAfEbEBcAsQ+MAWRUEuQwUIg9iLSgltArIUmBrLoE5H6O6CBgxOAosMSTewgkVHMBM3B6ICDSAeC9L9Gj05CRQSI/YVI35tDPYgOQB7eS4R+UyA+TEjRazS+NTRNEANAyWM+FvEiIK4lQr8XNEPgBU+hUQIDIIPXEOlAUNpJRBNjg5aLxORiYyC+QUhRMxDPhEYtKN0tBeJtWNSBcuV/tNy9DppJXKB8aahYIpH6GaBFGigHs0AzVwE0FlFANTQn10JD8yUWg7BZAFLnB3XkH6hluIonXA6UhWbKP9CQTyYm6kTxWEJs8UML/XiBARBfgUbFQOgnCEDpS5ye+gEG50vt3SyTWQAAAHF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+YTwvbWk+PG1vPiw8L21vPjxtaT5iPC9taT48bW8+LDwvbW8+PG1pPmM8L21pPjwvbWF0aD5SwOVgAAAAAElFTkSuQmCC)
is
maths-General
physics-
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
A disc is rolling (without slipping) on a horizontal surface
is its centre and
and
are two points equidistant from
. Let
,
and
be the magnitude of velocities of pints
and
respectively, then
![](data:image/png;base64,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)
physics-General
Physics-
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle
is
Physics-General
Physics-
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
A solid sphere of mass
rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is
. The kinetic energy of the sphere at the bottom is
Physics-General
Physics-
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
The moments of inertia of two freely rotating bodies
and
are
and
respectively.
and their angular momenta are equal. If
and
are their kinetic energies, then
Physics-General
biology
Famous palaeonotologist/Palaeobotanist of India was:
Famous palaeonotologist/Palaeobotanist of India was:
biologyGeneral
physics-
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
A small object of uniform density roll up a curved surface with an initial velocity
. If reaches up to a maximum height of
with respect to the initial position. The object is
![](data:image/png;base64,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)
physics-General