Maths-
General
Easy
Question
The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is
- a1/3x + b1/3y + (ab) = 0
- a1/3x + b1/3y + (ab)2/3 = 0
- b1/3x + a1/3y + (ab)1/3 = 0
- b1/3x – a1/3y – (ab)1/3 = 0
The correct answer is: a1/3x + b1/3y + (ab)2/3 = 0
Tangent of parabola y2 = 4ax is y = mx + a/m, which also touches to the parabola x2 = 4by
a/m = – bm2
m = –(a/b)1/3
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A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
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)
A light rod carries three equal masses A, B and C as shown in figure. What will be velocity of B in vertical position of rod, if it is released from horizontal position as shown in figure?
![](data:image/png;base64,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)
physics-General
physics-
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle
to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle
=
will be
![](data:image/png;base64,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)
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle
to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle
=
will be
![](data:image/png;base64,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)
physics-General
physics-
A 2m long rod of negligible mass is free to rotate about its centre. An object of mass 5 kg is threaded into the rod at a distance of 50 cm from its end in such a way that the object can move without friction. The rod is then released from its horizontal position. The speed of the rod's end in the rod's vertical position is (in m/s)
![](data:image/png;base64,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)
A 2m long rod of negligible mass is free to rotate about its centre. An object of mass 5 kg is threaded into the rod at a distance of 50 cm from its end in such a way that the object can move without friction. The rod is then released from its horizontal position. The speed of the rod's end in the rod's vertical position is (in m/s)
![](data:image/png;base64,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)
physics-General
physics-
A uniform solid disc of mass 1 kg and radius 1m is kept on a rough horizontal surface. Two forces of magnitude 2 N and 4 N have been applied on the disc as shown in the figure. Linear acceleration of the centre of mass of the disc is if there is no slipping
![](data:image/png;base64,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)
A uniform solid disc of mass 1 kg and radius 1m is kept on a rough horizontal surface. Two forces of magnitude 2 N and 4 N have been applied on the disc as shown in the figure. Linear acceleration of the centre of mass of the disc is if there is no slipping
![](data:image/png;base64,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)
physics-General
physics-
A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of
of its centre of mass and an angular velocity of
. The distance (in m) of instantaneous axis of rotation from its centre of mass is
![](data:image/png;base64,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)
A disc of radius R = 2m moves as shown in the figure, with a velocity of translation of
of its centre of mass and an angular velocity of
. The distance (in m) of instantaneous axis of rotation from its centre of mass is
![](data:image/png;base64,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)
physics-General
physics-
Three spools A, B and C are placed on rough ground and acted by equal force F. Then which of the following statement is incorrect?
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)
Three spools A, B and C are placed on rough ground and acted by equal force F. Then which of the following statement is incorrect?
![](data:image/png;base64,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)
physics-General
physics-
A uniform thin stick of length
and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is :
![](data:image/png;base64,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)
A uniform thin stick of length
and mass m is held horizontally with its end B hinged at a point B on the edge of a table. Point A is suddenly released. The acceleration of the centre of mass of the stick at the time of release, is :
![](data:image/png;base64,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)
physics-General
physics-
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Find the tension in the string when the block has maximum velocity.
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//mPPnz9PV1UUkEuH5559n0aJFZGRkYDabefbZZykvLyccDrN8+XK2bt06ZWty3gjXFF/MBo/l7E0VGzsxMZElS5bwy1/+UvhyDQYDq1atwmg0CusLk8nEpk2bKCwsnJAbPxQKceHCBU6fPs25c+fo6elBr9ezbds2ioqKKCgoIDMz8yvnobwVDA4O0tDQQHp6Onl5eVdNYNbr9ZSWll5xPSmVSgoLC4Xd7dFolIyMDJKSkoS1fElJCUajEZ/PR2pqKhKJ5KY3IMfWkvEIQ10zwyW2XysWT8nOzsZisUzbNY7T6RSK/MS2mcSIZVc0NTVRV1dHdXU1PT09KBQK8vLyWLJkCaWlpRiNxrhXvZrKnDp1itdffx2n08nzzz8vJEBPVfr6+jh9+jR+v5/8/HxmzpxJcnLybckBva7Z6fV6qaioQKfT0d/fT3Z2Nnq9HolEIswy10qCnSpEo1HOnj3L4OAgOTk5lJaWAuOz3NDQED09PULgtqamBq1Wy5IlS9iwYQNLliyZtjec283g4CCdnZ1s3LhxWmTs9Pb2snv3boaGhtiwYQPz588nPT0dvV5PamoqGo1m0oR4TfFJpVKsViu/+MUvaG1t5dChQ+zatYuBgQFCoRD33XcfGzZsICMjY1IGd6uI1ezfuXMnHR0dPPDAAyxcuFAog3DgwAH+9Kc/cf78edLS0nj44YfZsmUL2dnZ4iw3AWJ1Nfv7+ykrK5sWZrlWqxXW7omJiRw4cAC73c7s2bO56667mDNnzqTdRK675gsGg7hcLqxWKw899BCbN2+mtraW//iP/6C5uZmlS5dOysBuJW63mzfffJPq6mq+9rWvceedd3Lp0iXee+89PvjgA8bGxpg3bx7PPfccq1evJjk5+bq71kW+iMPhYGBgAKVSydy5c6dFulwoFMLr9WIwGFi7di0PPPAAQ0NDtLW1cejQITIzM+MnvqGhIXbu3IlMJqOwsJB58+ZhsViwWCxYrdYpf3fzer00NDSwc+dOsrOzCQQCvPbaa9TX1xMIBFi6dCmlpaXYbDYyMzMxmUxTas/XdGJwcJCxsTGsVmvcd5HcKH6/n8uXL3PhwgXkcjlr1qwhOztbSHafzB3v1xRfbNdwrLaGw+Hg0KFDOBwOXC7XlK4MBeM3j46ODnbv3k1zczN+v59QKCQEbufPn8+CBQvIz88nKSlpWlwsU5nh4WECgQBms3nafJZyuRy9Xo9CoSAUCnHmzBmqq6tJTk7GZrNN6nlc167S6XTccccdQqJsbW0tPT09jIyM4HQ6p3ScZWRkhLNnz/Lhhx8SDodpa2sjGAyydOlSVq5cycKFC8nOzkatVk+bi2UqEY1GCYfDeL1etFotIyMjBAIBofCv3++/oojUVEShUJCamorJZGL+/PnY7XY6Ojqw2+1EIhHS0tImzaF4XbNzbGyMCxcuYLVaycvLo7i4mLa2Ntrb2wkGg1M6t/Hy5cs0NTWhUChISkoSdhD4fD5OnDhBY2MjO3bswGq1TukLZKoSCAQYGBigubmZkpISnE4ngUAAg8GAx+OhqakJq9WK0Wicsp9vMBhkeHgYuVxOcnIyixcvRiqVMjg4yJkzZyb1va8783k8Hv785z/T1taGzWZj/fr1GAwGTCaTsItgqmKxWLjnnnuYN28eg4ODDA0N4XA4GBoaoquri4aGBr75zW+Ks96X5PLly+zatYs9e/bwyiuvMDIyQjAYRK1Wc+zYMX7yk5/wve99j+3btwvlA6caoVAIu93OqVOn6Ozs5K677mLFihXMmDGDzMzMSb1pXDfUYDQaeeKJJ3C73XR0dFBVVUVdXR2XLl0iPz9/Spc4NxgMaLVa8vPzCQaDhEKhK/4Nh8NkZGRM6XXrVMZisbB+/Xpef/11PvnkE3p6egiFQgwPD/Pmm2+Snp7OrFmzpnT7tFid0YKCAkpKShgZGeHll18GYOnSpaxZs2bSnC7XNTtDoRCjo6NkZ2djNBpJT08nKSmJrq4uoXPPVMPn8yGVSpHL5WLu5SSi0WjIz89n06ZNnDp1iqGhIaFxSmNjI08//TQ2m21Kh2zC4TB+v5+UlBRsNhtSqZTc3FwhG2oySxxdV3w+n48LFy7Q0NBASkoKGRkZlJaWcuzYMRISEqaULT88PExFRQVtbW1Eo1Fyc3MpLi6e8kkA05VYBeqHHnqIf//3f6erqwu73Y7dbqesrExoQjmVCYVCuFwuPB4P1dXVFBUVUVxcjFqtprOzc1Kzt64baohtVD179iwqlYrc3FwUCgWBQACNRjNl7mo+n4+LFy/ywgsv4HQ6kUgkzJo1i3vvvZevf/3rYqbKJKFWq1m+fDnz58+ns7OTgYEBDAYDjz/+OFlZWVP+c48V+e3p6aGiogKXy0V+fj5Wq5Xk5OT4rfkkEglJSUncd999bNu2jba2NsrLy9m7dy/nzp0jPz+f0dHRKbGnraOjg4MHD3L27FlefPFFMjMzefvtt9m9ezdr1qwhPT1ddKxMIps3b6a9vZ1Lly6xevVq7rjjDoApcW1ci1i/B5vNxoYNG+ju7ubgwYN0dnaycOFC/vmf/3nSeiZeU3zhcJjh4WEOHTrEsmXLsFgsbNu2DZvNxgsvvCB4idra2iZlcDdKNBrl1KlTvP/++2RmZhIOh4X+4B0dHTz//PNs2LBhyszSX0V8Pp9QPHjWrFn85S9/ifeQboiWlhYqKysxmUxs3LhR6OXgdrvp7e2dVG/+dbcUjYyMsG/fPrq6ulAoFMyaNQutVsurr75Ke3s7QNz3+kWjUex2O729vajVanJyclAoFAwNDeF0OlGpVJjNZtGrOck4HA7C4TAGg2HKm5sxRkdHGRgYICEhQdjBUlJSQn5+PqFQaFL9GtcNNWi1WkpKSkhISMDlcjE0NMTFixdpa2ujpaWF2bNnk5mZGdck2qGhIfx+Pzqd7op6Ibm5uXEb098j0/Hzdjgc2O12HA4HBoOBaDTKuXPnqK2txWg0smLFiviFGmKdYtasWUMkEqG1tZW+vj48Hg+jo6PMmzePNWvWfGFz6u2kvr6eixcvIpPJ2LJlS9zGITL9qK+vp6Ojg7GxMdavX09WVhY1NTU0NzfjdDqFfZ+TwTXFFzM79+7dy+LFi8nOziYvLw+FQkFFRQVdXV2TNrCJ4PF4CIfDpKSkxHsoItOMWPHlWJpZUVERmzZt4h/+4R9wOp2TmiBwTfHJZDL0ej1lZWXs37+fy5cvk52dfdWiOPEkFgwVA+oiE0UmkwlOlZdeeolDhw6xYsUK1q5di8Viie+uBo1GQ0lJCVlZWbhcLrq7u6moqKC2tha/3z9pA5sIgUCAaDQ6LcoWiEwtYsWWlUoljz32GDNnzqS1tZWXX34ZuVzO448/Tlpa2qS893XNzuHhYT7++GMKCwvJysrCbDYTCAQ4cOAA3d3dkzKoiRIOh4lGo2IoQWTChMNhRkdHCYfDWCwWioqKSEtLIysrS+gxP1lc92qNRCK4XC5qa2tpa2vDYDAIjSGnysUeMw2mYatBkTgTcyqGw2GqqqqIRqOYTCbmzZtHUlLSpIZMrhtqMBgMbNmyhWPHjlFdXS14P51O55RJqlYoFEgkEnw+X7yHIjLNkMvlJCQk4HA4uHjxIh6PB7PZjM1mY8aMGcyYMSM+m2lhfEFqMBi47777uO++++jq6uLDDz+kpaWFYDAoFB2NpxBVKhXRaFToaCoicqPEWsfJ5XIeffRRiouLqa6u5tChQ3R1dfHcc88JrcBvNddNL+vq6uLXv/41ZWVlLF++HKvVyvLlyykqKmJoaIj6+npCoVBcnR39/f309vbS2toqzn4iE6K3t5fu7m6CwSD9/f3MmzePsrIyiouLCQaDmEymSXvva6aXRaNRPB4PlZWV9PT00N/fL6yvDh8+THNzMxqNZlILi94Ifr8fu92O2+3GYrGQmJiIVColEAjg9XoJhUKkpKSIidUiX8Dj8dDd3Y1Op2PLli1YrVZMJhMlJSVCL8DJum6uKT4Yn5YDgQDNzc20tLQwPDxMb28vH3zwgTBIk8kUV2dHNBrl0qVLlJeXMzQ0xKOPPorBYODEiRM0NTVRWlpKUVHRlNp7+PdGJBLB5/PR39+Pz+e7ZZ2CpVIpSqWStLQ0tFrthL/j/v5+zpw5Q2pqKqtXr0ar1QqFn3Q6HRs2bJi07K0bKqBUV1dHUlISq1atAqCyspL9+/dTXFzMww8/TEFBwaQMbiLU1NSgUql46623mDVrFhaLhdbWVsLhMDt27BDFF0divfUqzp4FoxGXw0HoFpUfkSkU6AwGMvV65tls5MycOSGx1NbW4nQ60Wg0lJaWkpubi91u5/z587S1tU1qmZTrxvnsdjsvv/wy+fn5lJaWMmvWLIxGI7Nnz2b27NkkJCRM2uAmwpw5c9iyZQv79+/nxRdfRCaTEQqFmD9/PlKplEuXLsV7iH+3RKNRKqqr+X//9V/IV63CPzRExOeDW2AtSdRq5CYToZMn+fadd/JPDzzAooULb9hDOTY2RmtrK2NjY+Tn5yOXyzGbzdx5551oNJpJvWFf1+yMBSHPnj3L0aNH6ejoIBwOMzIywpYtW9i0adOUKdPg8Xioq6vj3/7t37h06RIKhQKDwSBmvsSZ9PR0QhkZ7E9JIfT97xPVaG6J8ACQSCAUgn37mHvkCA/l5/Pg5s3Mnj37hl5eX1/Prl27hJo/PT09yGQyli9fzl133UVycvKkxbOva3YCQm+0mTNnMjIyQl1dHf/zP/9DS0sLbrd7Ugb2ZdBqtRQVFfHiiy8yOjoqpA6JxJe6ujr+dPYs4WCQiFoNOh2Ew+BygcMBMhlYraBUjotpogQCoFAwPDzMwMDAhK/JWDx79erVJCQkMDg4yOXLl/nDH/4Qv53s0WgUh8PB7t27SUlJYc6cOWRnZxONRklPTyclJWVKtQeTSqVf2NMnEn9cLhey6mqisRjs8DB88gmcOQPB4Lh4LBa4916YOxe+zA0zGiUcCuHzeicUbvJ6vbS3t9Pc3ExOTg5lZWVYLBbMZjN9fX3xTS+DcdPT4XBQW1tLZ2cnTqcThUIx5cQnMk2oqYGTJ6G/H/LzYWwMysvBaBz/+ewyJmaefnZGvNpj/0cs6WMiRKNR/H6/4KBLSkrCaDQyd+7cSV2yXDe9zGQy8d3vfpeenh4qKys5e/YsXV1d9Pf343Q6p3yBnKlOLHldo9FM6erft5SODsjMhM2bYe3a8dnvZz8bf7y1FfR6aGuDtDQYHByfGZOSICUF+vrA4wG1GsxmuMkguEajIScnB71ej9Vqpb29ncHBQSwWCwsXLmTRokWTtlXtuman3+/H4XBgMpm4//772bp1K+fPn+dnP/sZfX19eL3eSRnYV51YMu/Y2Bj79u1j3rx5zJ8/P97Duj1s3To+e2k047OXXD4+242MgM8H1dXwyCPw2GPwzjtw+TKsXj3+ut/+FurqIDsb/uVfxp9zE4RCIcbGxjAYDCxfvpysrCycTieXLl3i+PHj2Gy2+InP4XDwm9/8hnA4zIIFC1i2bBk6nY6srCzy8/OnTKhhujE4OMjRo0d59dVX8Xq9/PjHP2bevHl/H1k4iYnj4pNKwe8fn+X27YO774aCgvHZz+UaXxv+8pdw/jzs3w+vvQZPPQUJCfDHP0JtLTQ0jL/mS+L3+2lra+PkyZO43W42bdrEnDlzWLBgAQUFBSQnJ9/CE7+S69btTE5O5sEHH8TlcjEwMMCHH35IV1cX3d3d+Hw+cRvPBHE6nZw+fZqPPvqIkydP0tjYCCC02r7ZLSyhUAiPx4PL5cJkMv1Nh4HH48HtdqNWq0lKSrq96YGx93K7x9d/v/0tFBfD0qXjpmZLy/hzliyBkhJQKKCzE3p6oKxs3FtaXj5uko6O3tRQVCoVWVlZZGRkkJ6eztmzZykvL8dgMFBaWopOp4tP9TIY366Tl5eHUqmku7ub5uZmvF6v0C56KjdKmUqEQiHOnz/PsWPH+PTTT2lsbKS/vx+VSsXw8DAejyzd/28AAAwCSURBVIdgMHjT4uvv7+fIkSPk5+eTnJwsiC8UCgldmmI7s9vb27l48SLbt2+//RaM3Q4VFfCXv4ybnV/72rinM+bgkMlg1qzxWTI5eXx9FwyOr/tksvHZz+WCm0xTk0qlqNVqzGYz8+fPx+v1ConWTU1N5OTkxK8t9NjYGGfOnEGv15OamsqKFSvIy8vj3Llzca/XOZ0Ih8NUVFTwySef4PF4SE5ORiqVYrVaOXr0KIFAgEAgcFNOF6/XS3NzM5988gmFhYVCjDMSieB2u6msrARAqVSSkpKC1+tl3759lJWVMWvWrNuXjODxQGXleLjB5Rpfuy1ePC6oGBIJqFTjQov9/tnZ+RZdd7HCSYFAgOLiYmw2G4sWLcLj8QgV8SaL65qdfr+fM2fO0NHRQXZ2NqWlpWi1WhISEkhLSxOzRyaAVqvlnnvuEfJlL126xKOPPkpDQ4Mgvpsh1gzUYrEIxY1hvJp0Z2cnx48fZ8uWLahUKhQKBRkZGVitVo4fP05SUtLtK4zV0AB79oybnd/9LsyePS5Cn2/cpLyNxMzt2tpaAoEA/f39lJSUYDabWb58efzifBKJBJPJxI9+9CN8Ph+1tbWcOHGCyspK2tvbmTNnzpQpojTVUSqVbN++ndraWn7/+9/T0dHBU089xezZs1GpVAQCgZv+LC9cuMC5c+d48MEHryhi3NrayqFDh1i3bh29vb1Cq7fU1FRWrlzJO++8w8KFC2+f+N59F06cGM9uOXfur7NbSQl84xtXzoCTTF5eHk899RQSiQSPx0NVVRW///3vCQQC3HHHHdx9992TVj7wumu+WNVqtVpNSUkJ2dnZrFmzhtraWjIyMsRyfTdIJBKhsbGRl19+meHhYR544AFWrlxJNBpFJpPd9Mzn8XhoaWmht7eX4uLiK0zO/v5+Ghoa+MY3vsGnn34qdOZJTEykuLiYZ599ltbWVmw226RVZ76CBx4Yd674/VeakqmpkJs7bm7+139Bevr437Ozx9eEY2N/ff7dd4PXCzd5w1Cr1WRlZSGRSITNs0uXLsXpdDI4OBjf0oExpFIper1eCEZmZ2cjlUqndNfRqYLL5aKqqoo33ngDj8cj3FFTU1Px+/3s2LGDmTNn3pRbe2BggJGRETQaDQaDQTCnhoeHGRkZQS6XC3VXDQYDEokEpVKJyWRCr9fT09OD3W6/PeIrLBw3NT/vKZfJ/prfuX49aLXj/09MHP9/JPLXtV5u7vjvCsV4nuiXJLYfEMadi1qtFrPZjM/nY2BgIP7pZZ9HqVROWl2LrxpdXV2cOHGC/fv3MzAwwObNm9m4cSM5OTnAuKt7+/btKBSKm/qih4aGhB37nw0bDA4O4nQ6MZlMOJ1OFixYINwwJRIJKpWK7Oxs3G43Tqfz5k72RrmR8/ys6SmT/dU0jfHZtMZbXLdHIpGg0WiYMWPGLT3u5xFT/m8hkUiEUCgk7KaQSCQ0NTWxd+9eLl++zA9/+ENWrFiBVCqlr69P6Bl4K8rcB4NB4aL5LA6HA5fLhcViEZIiPitOiUSCwWAApn4vva8aovhuIV6vF4fDgUwmIy0tDYVCgdVqZfv27RQXF5OZmYnP5+Ott95iYGCAn/70p7dsy5NGo0GpVDL6maBzrKJbKBTCZrMJa5vPEysOG89OU3+PiA3rbiGVlZU888wz9Pb2EgwGAZg5cyZr167FarUKjo6cnBxsNtstXcybTCYkEgl9fX1C1lEsSVir1WK1Wq/6fuFwmM7OThISEiZt/S6RSJDKZEQns4yHVIrk/36mC+LMN0HGxsYYGhpidHQUg8GA0WhEKpXidrvp7OwUWk5lZGQQjUYJhUIEAgGGhoYAMBgMwgwI47mFw8PDaLVaQqEQDocDpVKJ1Wq9ItslFArR29uL1+slNTUVpVKJx+MRtnWlpKSQmppKY2OjYNKmpKRQWlpKf38/ra2tjIyMoNPpsFqt6PV6QqEQTqeTkZERzGYzqampk/KZJSQkkKpWo2hqItDRcWtjeRIJBINI6uvRhcPotNpp05hTFN8E6O7u5tChQzQ0NBAMBlGpVJSWlrJs2TLa2tqoqKigp6eHPXv2kJiYSGpqKj09PTQ0NGC325HL5WzZsoWOjg6cTicFBQUMDAzw3nvvCbNST08PgUCAtWvXsnTpUtLS0rDb7VRWVlJeXk4oFCItLU1Yt23bto2MjAzBQdDc3ExVVRUbN25Er9cLaWaXL18Gxj16sde63W4hZGSxWCZtS5PVaqW0sJBjFy/S9ac/jfdGuEVpiVKFAo1ej+bCBQpTUpiRkTFtEj9E8d0gsb7vH3zwAS6XC6PRiN1up7m5GavVysjICCMjI/h8Pnp7e3G73YyNjXH48GFOnjxJZmYmOp2OoaEhysvL6erq4sEHH2RgYIC33noLlUpFbm6ukCLW3NyM0WgkMTGRixcvsmvXLpxOJ3q9ntbWVtrb24lEIqxcuVJYX86ePZvOzk4OHjzIsmXLSElJQaVSkZ6ejl6vJxqNCm2OI5EIAwMDHD58mHXr1v1Ns/RWYDabWVVWRm9PD3Xt7fS1teF1u29J+UC5SoXeYkGv1bJk3jyKCgunTZ9GUXwT4MiRI1gsFr71rW9RWlpKb28vL7zwAk6nkxUrVjA6Okp7ezu/+MUvmD9/PjU1NYyOjpKamsprr71GYmIibrebAwcOXHHcsbExli9fLrSjKi8v54knnqCzs5O0tDSqqqpob29n165dZGdnU11dzauvvsqJEyeuOE5ubi42m40PPviAvr4+EhISUKvVKBSKL5higUCAnp4eamtr+c53voPVap20z00ikZCXk8NTP/whdrud/v7+W5qUH4tZarVaLBbLpFaZvpWI4psAmZmZfPTRR1y4cIHS0lIWLlzIc889R3p6+t80dRISErBYLEIi9dVmF71eT2FhIXl5eQCUlpYKKWeNjY309vayfv16LBYLCoVC2FdZXV19xXFUKhVFRUU8+uijNDc3X3Ncg4ODBAIBvvOd7wjHnWykUilGo5GUlBShO9CtQiKRjDt2pNK4Vk+fCKL4bhCJRMLXv/51EhMTOX36NBUVFXz88ceYzWYef/xxVq5cedXXKZVKdDrdNS8IhUKBUqkUzEGlUolEIhEqCfh8PrRarSBehUIhzGifH6PRaGTdunVEIpFrei9NJhOLFy++amxwMplO4phsRPHdINFolP7+fnJzc8nIyMDpdNLe3s6hQ4c4derU38z4id2Nr8W11lqxEujt7e1CENzlcuFwOK5awkOhUNxQqTu1Wj1tHBNfVUTxTYBTp04JAeuSkhIyMjKoqqrC+3/l6qRSKZFIhJaWFqGz6c2SkZFBVlYWn376KX/5y1+wWCx0dnZy4sQJsSPTNEcU3wSQSCScPHmSmpoa8vPz8fv9OJ1O5s6dS3Z2Nn6/n+TkZI4ePUpmZibBYFAwFz97DK1WS2JiIhKJBJlMRmJi4hXZJbGEdZVKxcyZMykrK+PIkSPs3LmTrKwsent7qaurQ6PRCGsdkemH7Oc///nP4z2I6YBEIqG4uBiFQkFfXx9tbW1Eo1H+6Z/+iU2bNmGxWIT1WH19PWazGYPBgE6nw2g0UlxcDPy1VGBKSgqLFi0Saq4UFxcL++nC4TDd3d2UlpaSnZ1NRkYGa9euFV5bVlZGTk4OfX193HvvvZhMpmkTWBb5K9ft1SDyV2L96UdHRwmHw8hkMhISEtDpdMjlcgKBAB6PB4/HQ2JiIkqlklAoRDQaFbYLxY4RDocxGAxClolOpxOC3LEYnF6vZ3BwkIqKCi5evMiOHTuQyWQMDw/z7rvvsn//fj744AOSk5PFDkzTENHsnABSqZTk5OS/ue8uluZ1rSBv7Biffc3n41JSqRSz2QyMhyrC4TCffPIJ/f39JCYmCnv31qxZg16vF72H0xRRfFMcvV5PUVERd955Jz09PXg8HnQ6HYWFhaxZs0Y0N6cxotk5DYhEIoyNjdHS0oLP5xNqsIgFi6c3ovhEROKEuFgQEYkTovhEROKEKD4RkTghik9EJE6I4hMRiROi+ERE4oQoPhGROCGKT0QkTojiExGJE6L4RETihCg+EZE4IYpPRCROiOITEYkT/x+ZaYy1opn7/wAAAABJRU5ErkJggg==)
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Find the tension in the string when the block has maximum velocity.
![](data:image/png;base64,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)
physics-General
physics-
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Maximum possible velocity of ring of mass ‘m’ is (Assuming zero friction):
![](data:image/png;base64,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)
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Maximum possible velocity of ring of mass ‘m’ is (Assuming zero friction):
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAAB2CAYAAAAdi6VUAAAgAElEQVR4nO2deXBc5ZW3n9671Wr1plZr31qyFsuSd8t2JHC84GDAZAKEncAkzJAAk8xUUZU/pmqSSSozXyapLEWKCZMJMxgGE5jggI0dG2PjBS+yLcnaN2tpqSW1pFarpd6X7w9NX3DwhmVbC/epclnqvt393tb93fec8573HEksFoshIiIy75HO9gBERERuDKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRUQWCKKYRb7wxLf0h8NhhoaGaG9vJxqNzvKoPj+imEW+sExNTdHW1sbx48cJBoMEAgHq6+t57733CAaDsz28z40o5htINBrF5/Ph8XgQC7hcmlgsdtXvJhqNfuaYq73uau95qefHxsY4deoU77zzDj6fj0AgQENDA3v27CEUCl3TWOcSophvIMFgkAsXLnDmzJl5aabdbKLRKOFwmHA4fNnvJxaLEQwGiUQigpBisRihUIhIJHLZ973UDeBSx3wat9uNw+FgeHj4kuOJRCIXjWOuI5/tASwk/H4/DQ0NNDQ0sG7dOmQy2WwPaU4Qi8U4fvw4+/fvF250BQUFbNy4kW3btuHxeHj11VcZGBggOzub/fv3o9VqWbNmDcXFxezcuZOhoSHS0tK4/fbbeeCBBwCora3lwIEDnDhxgmg0Sk5ODtXV1Xz1q19FKpUyPDxMTU0N7733Hg6HA5VKxbJly9i+fTt5eXm89dZbvPnmm3i9Xp5//nkee+wxYrEYQ0ND/PrXv6alpQWfz0dpaSnf/OY3SUlJQaVSzfK3eXlk//RP//RPsz2IhUI0GiUUCpGYmEhRURFSqWj4xGIxxsfH2b17N+fOnaO4uJjk5GQmJycByM/PJxwO8+qrr9LS0kJBQQE6nY7u7m56enqYmJjAYDCQmJiIw+Ggp6eH6upq2tvbOXToEI2NjeTn55OSkoLH48HpdJKQkIDBYODw4cN88MEHSCQSsrKy0Gg0uFwuOjs7KSkpoauri76+PmKxGOvWraO0tJQLFy5w4sQJSktLMRqNBAIBhoaGkMlkZGRkkJiYOMvf6OURZ+brIBKJ4Ha78Xq9wj+AzMxMMjIySEpKQiqV4vP5GBsbY3JyEq1Wy+joKOFwGK1WS3p6OlqtFplMRigUwuPx0N/fTyAQQK1Wo9frGR8fx2KxYDKZUCqVs3zW10csFsPj8XDhwgWCwSD33HMParWaU6dOEY1G8Xg8JCYm4vf7UavVVFZWsmTJEl588UUOHDhAb28vP/nJT1Cr1bz88su8//77jIyM8PHHH9PW1kZGRgbf//73kUqlvP/++xw8eJB3330Xi8XCyZMnuXDhAi+88ALLly9nZGSE//3f/2Xnzp3ceeedLF++nMnJSZqamnj66adRKBQcPHgQuVzO2rVrWbVqFY2Njbz77rscOnSIVatWkZqaOttf6WURxXwd+Hw+jh07RnNzM42NjbS0tCCRSPiHf/gHBgcHOXXqFC+//DK9vb3s3r2bs2fPUl5ezjvvvIPL5WLp0qU899xzlJeXk5iYiNvt5sSJE/zyl7+kt7eXvLw8qqqqOHToEA8++CDbtm2b0xfRlZBIJOj1ehQKBWfPnuWFF15g8eLFrFmzhtWrV1NQUMDo6ChyuZysrCxWr16NRCLBZrPhdrsxGAxYrVbUajVWqxW9Xk84HKavr4/U1FRuv/12YbZctWoVExMTvPrqq2zcuJFYLEZ+fj5VVVUAaLVaysvLOXbsGHa7naSkJJRKJXK5HI1GQywWQy6XYzabWb9+PUlJSaSlpVFQUEBLS8ucj3CLYr4O4rPNkSNHkEgkfP3rX0en05GdnU1LSwsDAwNCIKenp4dz585hsVh45JFH6OnpoaWlhZ/+9Kf867/+K6mpqRw7doyf/exnrFy5kq1btzIxMcHx48c5f/48mzZtumzgZz4gkUjQarU89thjFBUVcf78efr7+/mP//gPDh48yEMPPURpaSlKpRKlUolEIhFeK5VKL+uqxANTn35eJpMhkUjw+XyEQiEkEgkymYxYLCa8r1QqRS6X4/f7SUhI+Mz7xoUdP/7T45nriGK+DmKxmBCVzcvLY+vWrcKdPRwO4/f7icViRKNRgsEgGo2GTZs2UVhYyODgIDKZjP/6r/9iYmICv99PW1sbSqWSjRs3YrPZGBsbIyEhgdOnTxMMBud1ZDzuMw8ODqJSqbj33ntxOp0cO3aMkZERzp49i81mu6xwLycms9nM0NAQLS0trFu3DqlUit1ux263k5OTg8ViIRaL4XQ66evrIy0tDZ/Ph8PhwOl0XjaYdalxzBdBi2KeASaTifz8fEpLSwEYHBz8zDFKpZLMzEzuuOMOZDIZqamp9Pf343K5CAaDDAwMMDg4yNKlS1m2bBnp6emEQiFMJhO/+93vFkQQLR7l7+3tJSUlBavVSl5eHjKZ7Loj/iUlJYyMjHDixAmys7ORyWScO3eOwcFBbrvtNrKyskhNTaW7u5tdu3ZRVFTExMQEDQ0N6HQ68vLyBLN5cHCQmpoa8vLybuRp33JEMc8AjUaDWq2+4jEqlUoIdEkkEuRyOQqFQnh+bGwMt9vNokWLkMun/xwKhQK9Xo9Go5n3y1sSiYT09HSMRiN/+tOf2LlzJ0lJScjlctatW8c3vvENtFotSqXyou9FJpOhUCguOn+5XI5KpUIikbB27VqGh4f5z//8T5566imUSiUpKSls2LCBr33taxiNRjZs2IDT6eTHP/4xBoOBUChESUkJjz/+uDBTS6VSzp49yz//8z/z93//9xd9Rnz8MpkMpVI552+sophngEQimbEJlpiYiFKppK+vj1AoBCBEt30+H+Fw+EYMdVaRSqXcc889LFu2DLvdjlQqxWQykZqaSmpqKlKplG9/+9vCzQygsrKS0tJSFAqFEMnftGkT5eXl5OTkoFar2b59O6tWrWJ4eJhwOIzJZCIjIwOj0YhcLqe4uJhnnnmG7du3Mz4+jlqtxmKxkJ6eLtyI77vvPsrLy5HJZBQXF7N06VIqKyuFm3RaWhpbtmxh2bJlc37mFsU8y+Tk5JCSksL777/P6dOn8Xq9uFwu9u/fz/j4+LzJProaFosFg8FAfn4+sVgMjUYjzICxWIzCwsKLboxmsxm/309HRwf19fWsXr2a1NRULBaLECiLL9v5fD4ikQgqleoiSykhIYHs7GzS09OZmppCoVCgUqkuumlkZmaSnJxMJBIRAl9Wq1WwCDQaDWlpaaSkpMz55UFRzNfJlWbkTz93uePis3pOTg5lZWUcPnyYjz76iPb2djweD2fPniUQCMyb4Mu1oFAoMBgMn3lcIpEIwah4ELGjo4OTJ09SV1eHXq+nuLiY1NTUi0xxmDbHr5TIIZFIUCgUaLVampubicViVFRUCM/L5fLPvP7TnxEPiP3l585FRDFfBxKJBLVajU6nQ6PRCI9LpVK0Wi1Go1HwjxMTE9Hr9Re9XqVSYbFYUCgUGI1G1qxZg9/v56233uKDDz7AYDBQXFyMVqtFLpfPeV/tRhFfzhscHGTHjh0cPHgQmUzGU089hVarndH7+nw+fv/73xOJRPjVr351A0c9d5CI/Zk/P/HMJa/Xi1qtxmg0AtP7YV0uF16vl6ysLEKhEG63m3A4THp6uvDaqakpIQ/Z7XZjt9sZGRkhJycHhUJBLBZjZGSEJ554gr/7u7/j8ccfR6fTzeYp3xK8Xi/Nzc385Cc/YWBggDVr1vDII4+Qn5+PTqe77OwYv4QvZ8XE8wK+//3vE4lEeOmll27aOcwm83pmnpycpK+vj2PHjpGWlsbU1BRNTU1otVpuv/12NBoNbW1t1NbWIpPJWLp0KWvXriUlJWVGnyuVStHr9Z+ZceVyORaLRfhdpVJ95rOkUik6nY6ioiIAnE4nLS0t7Nq1izvvvJOUlBTGx8epr6/HZDJhtVovmv0XKqFQiHPnzvHaa6/R29vLunXr2LhxI3q9npqaGgKBAJFIBKPRSFVVFaOjo7S2ttLR0YHP58Nms1FaWkpmZiaxWAyv10t9fT1tbW2EQiGWLFmCx+O56urDfGZei9nn89HV1cXOnTux2WzodDr6+/sZGRnB5XKh1+sZGxvD4XBgt9txOBxIpVLuuuuuOeOLJiQkoNFo8Hg8nDhxgsTERCGnO55o8umAzUKlq6uLo0ePcvbsWb70pS9x9913k5eXh91u54033sBsNmM0GsnIyKC4uJgDBw7Q0dHB5OQkoVCI9vZ2JiYmqKqqwmw2c/z4cU6fPs3AwABqtZqxsTH6+/ux2Wyzfao3jXntjEUiETweDy0tLbS3t2O1Wnn00UfJyspi165d7N27F6PRyN/8zd+wfPlyLly4wJ49e+ZUhDg5OZmqqiqee+45zGYzXq8XvV7PXXfdxXe+8x0hIWWhEovFCAQCHDx4kFOnTlFYWMj3vvc9qqqqSExMZGhoiN27d+P3+4XMrvr6el599VW6urpYtmwZt912G729vXz44YfCisCOHTtobW3FZrNRWVlJXV0ddrt9tk/3prIgbvnRaJS/+qu/4oEHHkAikRCNRunr66O8vJxvfetbaLVagsEgPp8Pl8s128P9DGazmQ0bNlBZWUk0GkUqlaJUKklISFjwwa9gMEhDQwMHDx5EIpHwzDPPYLFYhKWheDR6w4YNbN68mcHBQV5//XXKysqoqqpi48aNAOj1et5//33279+PzWbD6XSybds2Hn74YaRSKRaLBb/fP5unetOZ92KO+6ApKSmYzWZ8Pp+w/zUpKQmTySTs3FGr1XMyz1kmk5GQkHDJxP+FTCwWw+128+qrrxKJRFi7di2LFy++aMOFTCYjKSkJvV6PTqfD6XQyNDQkpGvGl5VsNhtyuZwLFy4wMjKCUqnEaDRiNBqJRCIUFhYKgcqFyry/7UskEjQajZBuJ5FIhJ0xcrn8ot0yN8tPDoVCDAwM0NXVhdPpvCmfsRCZmJigqamJY8eOkZeXR3V1NXq9/iJrJL4MGH8sPlOHQiEhYy5eVggQUkBDoRDBYFDIoLtSqaKFwryfmWH2drX4fD4mJycZGhri7NmzBINBysrKLopoi1yegYEBDh06RCQSYeXKlRclc3yaT/991Wo1+fn5QiTbZrMhkUiora0lFApRUFBASkoKfr+f3t5eurq60Gq11NfXMzIyMm/3hV8LC0LMs0EsFqO5uZl9+/axZ88e2tvbqa6unvGy1xcJu93O0aNHqa6uZtGiRddUX8tgMLB161b27dtHU1MT586dQ6fTsXfvXlauXMndd99NamoqRUVFHDp0iPr6ekpKSjh16hTt7e2imOcy8bTIv5ydLzVbz3RjRDQaZWhoiHPnzvHRRx/R3Nws7MR5+OGHKS0tpbCw8Lrf/4uE2+2mp6eHvr4+vv3tb5OVlfWZv41arSY7O5t7772XtLQ0YHrtPisri2effZa2tjbGx8eJRCI88cQTVFRUUFZWhkaj4a//+q85e/YsdrsdtVrNo48+Sm9vL1lZWbNxureEK4o5vsH+ZvqbM0Gr1VJYWChkCcF04kZ6ejrbtm0Tsq5gOtG/qqoKt9v9uc4lnmJ44cIFWlpaaGpqorW1lfHxcUwmE4sWLWL58uUsW7YMo9E4L3J45wL9/f309/ej0+koLi6+ZHAqLty77rpLELNUKiUhIYHq6moKCgoYGBggGAxSWFiI1WoVgohLly7FbDbjcDgIhUIUFhYyPj5+Q9bsY7EYkUhE2NY6V7hsOmc84d1utxOLxYTo8HzY13ktxDOKpFLpJbOCotEok5OTjI6OMjAwwJEjRzh58iQOhwO9Xs/GjRvZtGkTRUVFM8ob/qLy3nvvsXfvXtxuNz/96U/nlfk7NTVFT08PEokEnU6HXq8nMTFx1oV92dtUfDH/pZdeYnx8nPLycjZv3kx2dvaCSIkbGBjA7XaTkJDAokWLLnouFovh9/s5ceIEu3bt4v333ycQCFBVVcXzzz/Ppk2bhCJ1s/0HnK/09PTgdrspLy+f07WoL0V3dzc/+tGPGBwcZPXq1dx1112sWbNm1q+Hy4o5vuTz5JNPMjQ0xODgoNDGIxKJkJqayurVq1m8ePG8yh2Ouw6vv/46XV1dLFmyRBBzIBCgt7eXo0eP8tFHHwn+1te+9jVWr16NzWYjPT0dk8n0hUixvFlEo1H6+/vxer1UVFTMOzErlUrS0tJIS0vDbDZTV1fHn//8Z1JSUqioqKCkpGRWVjSueEXG99vG6zZpNBrGx8c5efIkfX19JCYmUlBQMK/E7PF4qKur4/Dhw+j1eqxWq7De2djYSHNzM93d3QCUlZWxePFiysvLKSkpQavVLggXYzaJRqO4XC5GRkaQy+WUlJTM+U3/f0k8Q89kMlFYWIjBYECn0xGLxejv70epVM49MYfDYaG9pV6vp6qqCrVazcTEBKdPn8bj8cyrhfhQKERfXx+vvfYaY2NjLFmyBIvFwsGDBzl69CgNDQ1MTU2Rm5vL5s2bWb9+Pbm5ufO+DtdcIhqNMjAwgN/vR6/Xk56ePu++33A4zMTEBNFolOLiYsrKyli3bh3Dw8O0tLTMWtroFX3mcDjMG2+8QWdnJ1lZWWzdupWVK1diMpnIzs4mNzd3Xt1V3W43dXV1/Pd//zf33nsv4XCYX//61/z5z38mMzOTO++8k69+9atUVVXN2Qj+fCcSiWC321GpVBeV55lPxKuq9vT0MDAwwOTkJJs2bSItLW1Wl74uK+Z4lPfpp59mdHSUoaEhmpqa2L9/P52dnSQmJrJkyZJ5MzPHm5e9/vrrKJVKDh8+TEpKCoWFhfzwhz9k5cqVZGdnk5ycLAr5JhKNRnE6ncjl8kuWEJoPaDQabDYbRUVFZGVl4fP5+OUvf4lMJqOsrIzly5dTUFBwy8d1xZk5Go0KS1Lp6emCWTQ5Ocn4+DgTExPzpttCe3s7NTU1NDc3E4lE8Pv9hMNhoZSqz+dDJpOh1WpFId9gIpEIU1NTQvuXuJj1er1QSOAvS+3OB+I+c0pKilBYMH6zmnNijkQitLS0EIlEMJlM5Obmsnz5clwuF2fOnJlXF73T6SQWi5Gbm4vBYECj0WAwGJDL5TQ3N9Pb24tCoSAtLU2MVN9AotEodrudtrY2FAoFy5cvF3pLqdVq+vv7OXv2LEVFReTm5s6LyHY4HBbKQWVnZ7No0SKht1U8eDobXDUD7MyZM5w5cwalUsn69esFf9JsNmO1WufNhZ+Tk8M999zD2rVrGR0dZWxsTPh/bGwMu91OZWXlvPTh5jKRSITDhw/z9ttvk5ycTFFREU6nUyhKf+DAAX7wgx/w3HPP8eijj86L3PZoNIrP5xO6dNjtdjZu3Ch0N5mtFY8r+sxKpZIHH3yQO++8k+HhYdra2vjtb39LU1MTGo2G4uLieWNmp6SkYDQahR5Rn/4XiUQIh8MkJyeLYr7ByOVyvvzlL3PmzBmhPerQ0BBGo5HOzk6OHDmCzWa7bErnXESlUpGZmUl+fj42m43ExETeffddXC6XUNlk1apVt3xcVzWzfT4fer1eKGKemppKMBhkZGREaJA2V4mLNd7qZD5F3hcK8aLyK1aswOFw8NZbb+FyuUhISCAUCjE8PMx3vvMdSkpK5o3PHNdFUlISOTk55ObmYjabcblcwjU3G1xVzB0dHUIjM4PBwLp16xgYGKC+vv6injxzjfb2drq7uxkbG0Mul1NYWEh2dva8jaDOZxQKBStXrqSnp4cXX3wRlUqF3+8nMTGRsrIyNm/eTEZGxmwP85qJRCJCIcELFy6QnJxMaWkpOp2O4eHhWVvhuWI6p1QqZXx8nI8//hi3201RURHV1dV4vV4SEhIwGo1zziyNV534wx/+wJ/+9Cd6e3uRyWTcf//93Hfffaxdu3bO3oAWMkVFRVRWVvLmm29it9sZGhqisrKSJ554gszMzHllNcW10dHRweDgIF1dXaxfv56ysjLMZvOsBfGuKGaFQiFkQo2NjdHd3c2+ffs4efIkMpmMgoKCOdfYzOv1UlNTw5EjR7BarXzzm99EqVSyY8cODAYDixcv/ky9a5Gbj0wmw2az8fjjj/Ob3/yGtLQ0qqurue222+ZVOjBMWxopKSlkZ2dTVlaGyWSirq6OPXv2kJKSwtq1a9m0adMtH9cVzexgMEhXVxcGg4Hs7GyMRqNQNK+jo4Pe3l7q6urmVLeFkZER/ud//geHw0F5eTkWi0XYA9vU1MSbb77J8uXLZ3uYX0i8Xi9WqxWbzUZqaippaWm0tbXN9rA+N729vXR0dGA2m1m1ahVlZWUYjUZKS0sJBAKz5spdNWmkr6+Pjo4ODAYDer2erKwssrOzaW9v59y5czidzjljIsViMcbHx9m/fz8wXZbmww8/BD7pgzw8PExjY+NsDvMLTSgUwufzCRteWltbZ3tIn5vR0VHq6+uFgLBerxdm5NkMCl/VzNbr9Rw7dozu7m4MBgNr167F4XDgcDhobW0VMqjmwm6iSCRCMBgkEAig1WppaWmhpaXlomPi7WBEZo9YLMaFCxdmexjXTTgcxuv1Mjg4iEQiYXR0lIqKClasWIHVap01S/WKjePim/T9fj8TExM4HA5OnDjBvn37OHPmDIFAgKeeegqbzTYnaj47nU7a2tro6Ojg9ttvJycnZ7aHJLIA6evr46233mJ4eJhnnnmGe++9l/r6empqapDL5VRWVvLAAw/c8nFddmaORqMEg0E+/vhjjEYjOTk5GAwGkpKSGBkZoaenB7vdjl6vJzk5eU6UzvH5fEilUlJSUkhJSRFL3orcFNxut1CTW6vVYrPZSEpKoqCgAJ/PR3Jy8qyM66q5mPEZube3F61WS0ZGBmazmaSkpFsxvs9FMBjE6/WSlJQ0bxIQROYn8ZhSa2srH3/8MWazmcLCQpRK5aylOF81nbOkpIQTJ05w9OhR/H4/5eXl9PX1EQwGb+U4r4lQKEQgEMBsNs+bnHGR+YdUKkWj0SCVSmlsbOS9994jKyuL5cuXk5WVNWuW6hWveKlUis1mIzs7m3vuuUdIIOnq6qKnp+dWjfGaiQfA1Gr1nEtmEVk4xIO+CoWCe+65h0ceeYTW1lY+/PBDxsbGWLp0KU8//fQtH9cVfeZAIMB7772HXq+npKSE9PR0qqqq6OrqEtaZ5xLRaJRoNDrn6hmLLCziZYOCwSASiQSj0cjSpUtJTU3F6/XOvXVmmL4DyeVyHA4HY2NjqNVqUlNTkclkQve9uUS8Y0U0Gp3TG0BE5jfxdM5YLEZLSwsHDhxAp9ORl5dHdnb2rAWDr+gzq1QqqqqqqK2t5dy5c/T29pKXl0dPTw9er/dWjvOaiJs+fr9/3mzNFJl/xCczl8uF3W7nxIkTqFQqXC4X+fn5ZGZmYrVab/m4rjozxxuBV1VV4ff7OXfuHLW1tTgcjls1xmtGqVQK5YDjLT5FRG4WcrmcrVu38q1vfYuBgQEOHDjAkSNHWLRoEc8+++ytH8/lnohGo/j9fnbs2IFaraaiooKioiLKy8spLy+nrq6O9vZ2zp8/z+jo6Jwo9zI6Osrg4CButxtAXGcWuSkMDg7icDjw+/1MTU0RDAaFSjaTk5Nzz8yGaVPbarUyOjrKuXPnOH/+PCaTiYmJCfR6PSaTiYGBAVwu15yIHgcCAcbHx3E4HAQCAUwmk5A3HgwGheW0uejvi8wfPB4PgUAAtVpNb28v+/btQ61WCz6zyWSalXFdtdTuli1baG1t5ezZs5w7dw6DwUBPTw9yuZzi4mJSU1ORy+VzIuAUi8XweDxMTEwwPDyMSqUiOzsbgNraWoLBIFar9aLukCJzj3glj2AweMNjH1KpFJlMRkJCwnX3hpqcnMTr9QpdP7u6upicnBQ28xQUFAjX3a3kqrnZ8Emv40gkQltbG//+7/9OQ0MDt912G3/7t387p8xZh8PBv/3bv7Fv3z6+8pWv8IMf/ACpVMo3vvENEhISeOqpp1i/fr24dDVHiXffbGtrY2Bg4IYHWuObh0pKSkhOTr4u97Crq4vf//73mEwmqqurqaiowO1288EHH1BTU0NmZibPP//8DR33tXBVn/m3v/0tAOXl5SxfvpzMzExKS0uJxWLX3O3+VmI0Gnn88cdpaWnh4MGDQk+j7u5uNmzYgMViEXa7iMwtIpEI9v5+/t8vfsFIQgL+WIzA2BjcQKtPmpiISq9H+atfcfeXv8zWzZtZXFr6ua6HqakpmpqaCIfDKBQKjEYjWVlZbNiwgVWrVs3NSiNxU9rpdNLX10dPTw8ajYbu7m7kcvmcLBivVCopKiri61//Ovv27ePs2bNCkfWuri7eeuutOTdmkWnUajV+qZRjfj+elSuJZGQQ8XpvqJglKhVSqZTokSOoOjvR6fUY/29f8rXGfRQKBQaDgXA4zOjoKB999BESiUSo2DnnfOb4fuZNmzbR399PY2MjtbW1Qq8gmUwmNM+aS8R9/bvvvhu9Xo9Op8PlcgmN4ufikprIJ4wDvrw8/Bs3Eq2omH4wGgW/HyIRkMlAo4GZ3JCnpkClon3vXuoaGqj4vxas1ypmpVJJeno6KpVK6GRht9txu914vV5CodBnen7fCq5aacTv92OxWNiyZQt33HEHLpeL3/zmN9TU1NDT0zNn13ONRiPbt29n+/btsz0UkWvk9OnT/Mcf/kDM4yEWDk/PyJEIeL3Q1zf9v1YLOTmgVk8L+3qJRPBOTDAeCuHxeD5XADdeNFKn07Fy5UpWrFhBOBzm7NmznD59GpfLNffE7Pf7efHFF/F4PBQXF7Nu3TqsVitZWVm43W5hy5eIyE3B44G6Ovj5z6dFHYlMC9xshu99D5YsgRludY1vzvk8YvZ6vbS1teHxePB6vUgkEsrLyykrKyM/P3/WlmmvamavXr2a4eFhAoEAB6KprekAABAFSURBVA4cAKCxsZFoNHrdoX0RkWuipwc+/hhUKli5clrEDgccPAi1tWAyQW7uJ8fHYtP/JJJPzPD4Y5cpaxW3QD8PCoVCaAohlUqFKiNms5mCggLy8vKu94xnxFXFvH79etxuN93d3dTW1uJ0OhkZGUEikeB2u8Uc6JtA3IwbGBjAZDLNyUIQt4RIZNqcvusu2LAB0tKgrQ2am6fNbocDdDo4dWra9B4fB6dz2qcuLga3GwYGpn3k5GRYtAhuQM60QqHAbDYLBS4VCgWtra14vV4ikQgymWxWWu1ctdn68PAwCoWC0tJSKioqiEajvPTSS5w8eZKRkRFRzDeYcDiMz+djaGiIvXv3Ul1dTXl5+WwPa3YoLobsbFAqpwUK0z/H8xpCIWhthW99C554Ajo64ORJSEyE55+H9vbpWdxun36v734X7rxzxsOKd7RISEggOzubVatWIZPJ6Ovr49y5c/T19VERD97dQq4q5p07d9LX10daWhpf+tKXhKLf2dnZ5OXlieV5bjCdnZ3s27ePP/7xj4TDYfLy8liyZMkX051RqaZ94rjZ7HLB+fOweze88ALk50NX17RvPT4ODz4IDzwAr70Gv/sdbNoEP/nJtOj/5V+gsREWL4YZtsIJBoM4HA5qa2sZHBzE5XKxdu1arFYrmzZtmrW/1VXN7OrqaoaHh/F4PDQ2NnLq1CkaGxuRSCTirHyDiDfi++CDDzh69Chnzpyho6MDqVTK6OgokUjkhpVB8nq9TE5OIpVKr1h4zuv1MjExgVKpJDExcXYCnRLJJxHr4WH44IPpmXbzZli6dNp07uqaXroqLZ1+LBKZnq2npqbFvmoV+HzT5nU0Ov3zDFEqlVitVsxmM5mZmTidTl577TWUSqXQ0XI2yu1edaNFcXExhYWFuFwu6uvr6erqEjrEezyeObfOPN8YHByktbWVmpoajh49SmtrK6Ojo0JMYnJykmAweEPEHIlEOHPmDLFYjMzMzIvEHAwG8Xg8eDweTCYTkUiEoaEhOjo6WLVq1azkGgPTs6rTCR9+CCdOTAeyHnoICgqm/WmYFn1+/rRg3e5p0zwtbdocNxqnX6PXT8/yN+B6lUqlaLVakpOTKS4uJjExkYaGBiYnJ+nr6yMpKWlWvq8rmtnxLndqtRqz2czGjRvZtm0bv/vd7zh16pQgapHrp6mpiZ07d7Jnzx6h8qnJZMLv99PY2Cjs9pppXfJ4zvM777wjdMSME+8E0tLSgtPppLy8nOTkZAKBADt27ECr1WK1Wm99mmIkAmNjcOgQvPnmtEAfeQTWrv1sdFqlgvgNTyKZfv7T5u4NNH3D4TDj4+PC/vkVK1awfv16Ic1ztizWK5rZsViM48eP09jYiEajYfXq1axfvx61Wo3VaiUjI0P0mWdILBYjOzubp59+GqlUyocffohcLufhhx/mhz/8IcFg8IYk5kxMTFBXV4dEIiErK4vMzEzhuUAgwIULF/joo4/YunWrUHkyIyOD9PR0Ojs7ycjIYMmSJTMex+fC5YLTp+HFF+FrX5s2rwsKLrvMdKuIRqNMTU1x5MgRenp66Ozs5PbbbycrK4sVK1bM2riu6jPfdtttlJaW4na7cblcvPHGG9TW1hKLxViyZIk4M8+QxYsXo9Vq6ezs5I033iA9PZ1169axaNEilEql0G5npgwODvLOO+9gs9nIycm5yGxvaGigo6ODvLw8RkdHL2pLumbNGhobG2loaLj1Ym5pgbffnvaL9+yBhgaIWyiLFkFV1a0dz/9htVp58MEHhYSRSCTC/v37CQQCQmfIkpKSWz6uKzpiMpmMkpISFi1axPj4OO3t7bS0tJCeni50VpwLPabmMxqNhmAwSE1NDYFAgNWrV7Nhwwa8Xi9SqfSiogrXS3zN+vDhw2zcuPGi/dyxWIzm5mYGBwfZsmULnZ2dRCIRISFoxYoVHDp0iKamJqGKxi2L1qpU05Hnr3xl2oSWSiHeQjieDWaxwH33TfvLUun0ElZuLqxZ80nUWqGA1aunj7kB6796vZ6qqiqkUimBQIChoSEaGhoYGRnB4/Hgcrlm/BnXwzVFVWQyGWazGbPZTGVlJT09PQwPD6NWq0Uz+zqJxWJMTk5SV1fH7t272bt3L08++SSbNm0iPz+fnp4ecnNz0el0MxbP5OQkg4OD2O12rFarUAo2FosJDdA8Hg8Wi0Uo6hBvBmiz2QiFQvT19eFwOG5tuuLixdPBrEv1AFeppvO0pVL40Y+ms8NksukkkmXLpqPb8bVptRruv3/6hqBWwwxvjnK5XOjxrdPpSE5OZvHixYRCIbq7u2etZ/l1hUgzMzNJT08XioGLfH6i0SiHDx/mlVdeob+/n6effpr7779f2IqXmZnJL37xC0wm04yLP4yOjjIyMkJGRobgD8N0dLurqwulUolCoaC+vp6KigrMZjMw7WqpVCoyMjJwOp10dHSQk5Nz6/7mGs0nEeu/zJ3+dMpmauonv8d3VanVnzwfj2bHf79J3VgUCgX5+flzr6XrlZDJZKKIZ0BPTw9/+MMf+PDDDzGZTDzxxBPccccdpKSkCL6sUqmksLAQuVw+Y+vH5/MRCAQwGo0X+crRaBS73U44HMZsNpOeno5er7/o8+JF3j0eD263+9ZeqJ8W7NWOu9rrbpE7OJu6EBsy3WTiPq9EIhHa5gSDQcbGxsjPzxdWCCwWC0eOHCEvL4+8vDxhLfNGELeg5HL5RSZ7JBLB4XCgUCjIyckhMzMTlUr1GbNeoVCgUCjE+MgcRxTzTWZgYICBgQHS09MFE9poNFJdXY3NZiM1NRW1Wo3T6eT9999n8+bNN9yU1Wg0aDQapqamhDXQSCTC1NQUTqeTlJQUcnNzL1shw+/3I5FI0Ov1N1XQwk3kVgXYrnXmnyeIt9qbzP79+/nZz37G8PCwsF5sNpvZtGkTNpuNxMREoTpKRUUFqampNzxabDAY0Ol09PX1CctcHo+H1tZW/H4/RqNR8JMvxcjICMFg8KaM7dNIJBKkMhkxmYzYzRaZVIpEKl1QOe/izDxDAoEAbrebwcFBEhMTha1xMB14Gh4exul00tvbS1paGvBJI/v4ljm1Wo1er2fRokWYzWahwsvY2BhJSUmEw2GGhoZQKBRYrdbP5P2Oj48zMjKC3+8nKyuLSCSC3+8X6obrdDqsViuJiYmMjIwwMTGBVqulqKiIhIQERkdHOX/+PL29vSQkJJCZmYnBYBBSdicmJjAYDDc9+JWQkECq0Yi6oQFvZyfR//sebygSCUxOImloQOv3k5SaeknXYj4iinkGDA8Pc+bMGY4fP47f7wcgOzubFStWsGbNGk6dOkV9fT09PT388Y9/RK1Wk5aWxujoKE1NTTidTiKRCIsWLWLLli3s27eP6upqkpKSsNvtvPPOO4LfPDAwgM/nY/ny5VRWVlJcXAxAfX09J0+epKmpCalUSnp6OoFAAI1Gw7333ktaWhpqtZqUlBQqKiro7OwkOzuboqIiTCYTCQkJ2O12XC4XSqUSrVYrBMACgQD19fVoNBqysrJISkq6qRe9xWJh1dKllNXW0nbyJOMNDQQ8nhv6GXK1GrVajaa5mWK9nvycHDQajSjmLzrNzc3s27ePI0eOUFBQgMvlorm5WchvHhoaYmxsjKmpKS5cuMDY2BjRaJTa2lrefvttTCYTiYmJqFQqxsbGeO211zAYDJSUlNDT08OOHTuwWCxkZmYSCATo7Oykvb2dSCRCQUEBPp+P/fv3c/ToUdxuN3q9nsbGRnp6ejAYDFRWVmI2m1Gr1SQnJ7N582bOnz9Pbm4uNpsNuVxOQkICWVlZWK1WJBKJYPbHGwocOnSI9PR0ysvLb3oAzGw2s3rFCu7t6KC2vZ3e+nrcDgeRG5hlqExMJCklBZ1czsqiIpaUlpKcnLwggnuimGfAxx9/jNfr5bvf/S73338/U1NTvP322xw/fpyRkREeeughPB4PEomEH/7whyxevJjOzk5OnDiBw+Hg5z//OWvWrEEqldLX13fRBRWLxZiYmOArX/kKTz75JHl5eRw7dowf//jH1NTUcN9999Ha2srhw4cpKirihRdewGw2s3v3bl5++WX6+vouGmtKSgpbt25l165dtLe3U1lZKSSPxANknyZeRvaDDz7g2WefZc2aNTf9+5RIJCSbzfzdt7+Ny+ViaGgIp9OJ1+u9oUtiEolEsEKsViuZmZkLYqlVFPMMsFgs1NTU8Morr9Da2kphYSF5eXmsXbuW1NTUy64Pq1Qq0tLSMJlMaDSaS26kkEgkJCUlUVxcTF5eHiqVivLycoxGI+FwmLGxMY4ePUpGRgbl5eVCPap169Zx6tQpRkdHL3o/uVyOyWTi4YcfBqC7u5ulS5de9tziYnrooYdYsmQJ6njyxi1Cp9OhVqtJT0+/KbuQpFIpUqkUpVK5IGZlEMU8I1atWsXk5CRHjx6lrq6O8+fPk5KSQnl5OTqdjtTU1Eu+Ti6XYzAYhHXnS6X/xbOvkpKS0Gq1xGIxIaEjFosRDAaFoJhOpxNuHGazWeiBdKn3W79+PV6v96pbKjUaDdnZ2WRmZpKamnrLL3i5XI5cLv+MxSByeUQxzwCLxcLy5ctJSEigq6uLrq4uGhoaaG9vx2KxsGHDhku+Lj4jXC3oIpPJLjpGIpEIv8fFOTIywuTkpHCMz+e7bLP5eNeFa0Gn081KtQyR60cU8ww4efIkHo+HdevW8dhjj+Hz+di7dy+7du3i4MGDFxXii0QiRKPRG+b7KZVKcnNzhQJyPp8PmUxGb28vdrv9IoGLfDEQxTwDhoeHOXToEPv27WPDhg1IJBJOnjyJw+Fgy5YtGAwGlEolPp+PPXv2CD/fCHQ6HZs3b+bo0aMcOHCAgYEBbDabUENstvodicweophnwLJly3C73dTV1VFTU4NCoUCj0bB161bWr1+PwWAgPz+fiooKent76e3txWg0kpaWRnFxsRBUiudtL1myBKvVKmyxW7x48UWilEgkFBQUoNVqBX/6vvvu48yZMwwODtLe3k5WVhbj4+MEAoHP5GKLLGxEMc+A8vJyEhISsFqtDA4OIpfLhUoThYWFQkHEUChEY2MjBoMBi8WCXq/HaDQKmWIymYykpCS2b99OSUkJGo2GjIwMtm3bRu6nOjbIZDKqq6uFCOzY2BgWi4XVq1fj8XgYHh4mJyeHSCRCU1MTSUlJN6yqp8jc54rN1kXmLpOTk5w6dYrdu3dTUFDA/fffj0wmo729nVdeeYXu7m7efPNNNBrNglhDFbk6opjnKaFQiJGREf7xH/+R2tpaoX1tT08PqampbN26leeee27BrKGKXB1RzPOU+Frz0aNHaWhowOl0CnXZCgoKKC8vn5W2oiKzhyjmeU487XJ4eJhwOIzVasVoNIrJFl9ARDGLiCwQRIdKRGSBIIpZRGSBIIpZRGSBIIpZRGSBIIpZRGSBIIpZRGSBIIpZRGSB8P8BEgeP/E1drEEAAAAASUVORK5CYII=)
physics-General
physics-
On producing the waves of frequency 1000 Hz in a Kundt’s tube, the total distance between 6 successive nodes is
Speed of sound in the gas filled in the tube is
On producing the waves of frequency 1000 Hz in a Kundt’s tube, the total distance between 6 successive nodes is
Speed of sound in the gas filled in the tube is
physics-General