Physics-
General
Easy
Question
A smooth ball 'A' moving with velocity 'V' collides with another smooth identical ball at rest. After collision both the balls move with same speed with angle between their velocities
. No external force acts on the system of balls. The speed of each ball after the collision is
![](data:image/png;base64,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)
The correct answer is: ![fraction numerator V over denominator 3 end fraction](data:image/png;base64,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)
Related Questions to study
physics-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is
at time t, then the displacement of the left block at this instant is :
![](data:image/png;base64,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)
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is
at time t, then the displacement of the left block at this instant is :
![](data:image/png;base64,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)
physics-General
physics-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is
at time t, then the displacement of the right block at this instant is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAABKCAYAAADzPmsKAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA/zSURBVHhe7d1FjGxVEwfw897D3d3d3d0taFiwYcMOQiBAwopAvi0kBDas2cAGAkGCBgvu7u7u7t/H79D10jQ9PTN3em7PfFP/5OROXzlSVf+qOuee+968//6FkkgkJoX5nWMikZgEMuK0ACL+7bff6t/z588vCxYsKPPmzau/E7MTGXFawB9//FF++OGH8v3335eff/65/k7MbmTEaQHffPNNefTRR8uff/5Z1l577VpWXHHFztXEbERGnBYg2jz99NPlqaeeKu+++26NPPzV77//XosIlP5rdiGJMyKY83z++ee1iEgxB0rMDiRxWobI8tlnn5UXX3yx3H///eXVV1+tUUcal5g9SOKMAK+88kq5/fbbyxVXXFEef/zxssgii9TVtsTsQWqrRXzyySflgQceKA8++GD9+8gjjyx77713WWqppeoSdWL2oNVVNelIpCWjngzz8oy1DU//4YcfliuvvLI8//zz5YsvvqiLAxtttFE555xzyiabbFKWWGKJzp3t4qeffipff/11XZwYVarofRZdWGUclRyaoFXiUNSXX35Zj7/++mvnbPtAFopadtlly5JLLjntLyODOM8991xdDCCDDTbYoJx77rlliy22KEsvvXTnznbxwgsvlNtuu618++23VSejANKsvPLK5bjjjisbb7xx5+zMR6vEeeedd8pDDz1Ufvzxxxp5RpHX867a3XzzzcuGG25Y1lxzzaq86UQQ5/333y+LLrpoJQ7C7rLLLmXnnXcu2223XefOdnHPPfeUyy67rKywwgrViYwCX331VZXJ6aefXrbffvvO2ZmPVolz3333lUsvvbT88ssvNU0axaQ4POtBBx1U9tprr7LjjjuWxRdfvJ6bLgRxkHbbbbetqZpzFgYOPvjgcsopp4xkC871119fzj///HLooYdWAo8CTzzxRPnggw9q9B1VH5qgVeLwcBdffHFNUzbddNPqddueFIt6jJZ322mnnaqypps4H330Ubnqqqsqcbbeeuuy6qqr1qhzzTXXVFkccsghNfqttNJKnSfaQRDnxBNPLPvuu2/nbLvgTF9//fVy9tlnV33MFrRKnLvvvrtcdNFFZc8996zeXnow3WlSL8wzTNJNynl/6dJ0E8eCgLGbgCMIskhXr7vuutq2tHGrrbYqq6++eueJdhDEOfnkk2vkGwXuuuuu+k7rzDPPrNF/tiCXo1vA8ssvX1NDxrnlllvWOcUaa6xRTjrppHLCCSfUqNd2tElMDUmcFiCqIobVo2WWWaZOhkUa5BFllltuuXouMXuQxJkErARa2PBpgL8Dsl1pmCV2iw/mMt1wzTOeda07O3bNPrW43ps5a0dap+5+1/r1JzEYZB5y6y3O04d7BmHBf/5C5+9px9tvv13fnK+77rq18Lptr6p9+umntYgAvP1aa601oXkWQXrjf+edd9ZPBBBgvfXWq9cYtcn+TTfdVK699tqyzjrrlFVWWaVeg48//rhcfvnldW5lQWSxxRarR7BY8fDDD5ebb7657lvrfSFqV/Ull1xSiSFCda9E6s8dd9xRHnvssdqH9ddfv56fKGz9MfeyHO6F7Cjw1ltv1b17u+++e301MN1ACotD5G2voFW97vLmm2/WOan596D3axlxJgje/uWXX64rg4z1tdde61z5e4nbkioDNtm1ihYRAMG8q2DkFMVY7YYOuNe7LfU++eST9WWkZ7WHDD5DsK/NJwkIyCMGEM1z2vR3YnyQrZfQVvPoC4m6C6dqN8V4u9WTOBMEQ+aJvMQkYAYe8L0NT4UQltcRSXoVxh/vjr777rtq4N3EocSXXnqppgkiiWvuF+G87/G3yKztN954Y2FdgJD6g3zd/UmMDXKlL9mPqH/44Yf/o9g7uM0229R55yAkcSYAwkaAyH+lS2HYPJijCIQoUlAGzZjdgxg2dK622mqVAEEc90Yd0jypncWD9957r5JEvQjqujRK+4iDkKKYvkR/1OUcUjnOVZDHM888U6N7bG/qh5AXcngV0F3IWko83r65GU0chqXEQBmTo9/Qfc59E0G3kTFgRstQ+xXX1c9oGbDnGH989uweynJNxDF3sd/KeambtqRXSIRQlqXdJzqoKyak6jcv8mI0cn7tStN4R+941OVZ/UYW0Sv6E7m4/qrL9fHGpkQdIedB0L6x6q/69cO4o//OIbVz0ce2EcSRvppLc1LGSYa9/bFTw0qmnendxaonQo03752xiwMUZcAUY5CMjRAo2m/PyUWdozjnGO54YIzmKgxUisQzmZzzUr2FoTJo9fP2CECgFhTivQsSMfRbb721jsmOBKTRP7sEKJICTdz13VvymAiLKGTCgL3LQSx9Ep38uwT64JoXtdrWjpfH+qBOpNQOwnnG+CmeTOxKsJAhl+8dVxS68PIRMb2UHbRbnOHZFKq/SO05CxdIQk908eyzz1Z5irj0MZF/V2GYiwP6KHUl43vvvbcuxpBnOBjvz+KeW265pbZLVrY+RTE2EWe8nfMzljg8oPsZOs/JcBikowkcz+Y3ISgUyFOob9A2HsaqTgLiceIZiu4u7uO1bQ1CWoYCUipGrX/6Ib1yHfkYOOKY5MNuu+1WHnnkkWrku+66a+2XMTFU+TViMjgRY4cddqjXGTTZSBlM+pF2v/32qykcRbvPWBmofmofcZBJXcZDXp5FOl60d2xR3GdVz1YX4ySPsfTBm1vEYOjukQYpYXyijWPoyj3k5DhWncAh6QOS0alxNi3qQRp1co50qOib/usHEumnBR6/kRWZonCKVksHyQLa3e8yCRggj8HLgUEwVkbvb1tXHAnFOfkpj22J2XEsICvjF0k222yzaoj9IpXtKOYtyIFAPJe3/oTKq4skPKxIIjoyXgbPWyFSzIMoiXGJUPJmbTJ8q2sUzLARyXiMgzF6HrG17ToD1K65Em9uzOQiojlPDgyasfCq2lb22GOPcthhh3VG9G/4pIBDIC/tDDKUSB0VdTM4UUqkZZTkbyld+86RCUfit7rHgnrJ5+qrr57yS2BtMn7OhkMhKzKjS/oyVrs3jJMd0MXRRx/defpvxPxmkCxg8NURIoTAM0pDKMH+NobCO1EIQ3YuNowSEqMcBPXx7JTJYOKNfm9hFIyD92TkPJlnzGGQRR2MCLl4evcjDxLqG9KINIzcOwHKQFjf3ziHiAyd4VCgZ4zBPa7HcnfsNKBQZDdGz+mPOo1dnxizc/qKfOSk9BtbFP0yDkYynqEAZ6aP2tRnciBD40Zi5zkPMtVnabZnBkH76qDHY489dkrlmGOOKUcccUTdf0iOgNQhdxkAneqbwo7Irru4V5/YySDMWOIEGCsFSYF4UF6NBxZSLRs6F/u/eBjKGg+EwlAYWwixt6hfEepFBvMJRsN4RTX3IIx0S1RBHEJXJ6ITPi/H+/nNyCmKZ0YMpJJaIJjxSdfUz/AiomiDgetrEEc/oj/qdE5BWOcQDnGC+N1j6i1hIOMZSTeQDWlESH0yJseYJ5ENOdAbp2B8gxDEsTvbvr2pFORBDn3TT/WSgfnjPvvsU9tgO8ZOT5wS3XSXcCaznjgGKG9nJAbjtzDL0AgADHQiHnMyYAyEbv4kZYqoEW3pE0GLSKIAZTEYBsyA9NH8huHwZEhBkbwyYohWIqr7XVMvRTLKWB3SBkW7xiARxLwOQdSlP+Sh+JtMoj/IKBIMG3QQpAs41y3/yRAR3E9eyDaVIkuxGKLIPHxndN5555XTTjutfrohEmpnGJjxxKEQxhWK8tvf3coj+MkqazwwWkVU4TkZMMMMAxHhpEJWlMyBkMj9+sVoEU06xqiDOJRGedKXWMzo9nBBHAYgqvDmyBJE9Vt/RDHnPRtj9yyyI51JtnudGza0Ff3tRb9zE0HUGU6gaSFfzk708yJz//33r1FGmk9/rtMPuUndyLApZjxxgGCbKqUpCFlhiLy5FJHxBqRQziGBCMJQeb0gjohgwu5ZK2SIgwCuA2dAcYgUYOgiEiMSWbQREUc96pCKqgPBtBHwt3ZcE8ncr425BPI7/vjjyxlnnFFOPfXUmp5FFhBAME5OBJrKJ+szmjiMwKAZXBDHwCMCBaGcc69jRIRhABmswphwyp0pISAN8uGVaxTEqEH7PBrDdo1yECAIo79ybhPZAw44oKZ4Af1HTs9YDTMfEtli7K4deOCBtV7L292pmGhjvnfUUUfV5WvRcZjQN8QUPY1Fn+hB/zkKRKUTzsZvTqE7nW4D+qR9fdFut90E9JFMzZml1E0xo1+AmuRSmEk6oyEMCwCOjIZhq8PyrXPucX5QimK+ovD04+2OJnTKZxyETOBhCI4Iog/GIkVQj2dcMy4RSNrgWowzrmuXIepDN+mifv3zrGMo31Gd+qJP2o77g3Tqk0I6jjWuwGR2R9OHlFV/kDTqNodzjtwRSR/d65xCP4x1LAzzBShoP+TVD66RGV1OxbnM2IhDMTy6HJUhIAMldK+uxQTZUigv7siYhgUGLXLEMqW2AoxEW3Jl6VUYcEA6oO/98mikEU2kYYy9F4hhhwDD64b2taX09kdfkcU1pNK/YcL4yEK/w+E50kOkohFxyCt01iuX/xfMWOLwDLwCA+FlEYmykIVBRRpAWYyPETsO02DUTfmKeiNqQEQHUcf17mvAgPQ9okk3nPOMY7+oYLzG2DsWbYzVnzBa18imtz9TBX1E21F39Ed72nePo9+hs0HefzZjuNJNJOYIkjiJRAMkcRKJBkjiJBINkMRJJBogiZNINEASJ5FogNb/7egLL7ywbl/xEtM7gH7vMaYTtuv7oMnLPG/M2/i3o2cqbrjhhnLBBRfU/xmOTkYB/0STHehnnXVW/qPrY8HnvIjj7T8heVHWNnFsM/HNiu0svv6cy8S58cYbix1X3vTbxTAK+AyCCfpvPuhitmAhcezytWfIh1s+zrLDdthQt3/gwVtl0cab92G/4R4Pvom3383GS1tfbEhsm7wzBT578O293Q90MgrYWW63gc2rU9nmP0ywB44kSj/7WEgcROGJGXZ8CDRsUA6D9SGWDZyjAKLaBsJREIg+/b9uCxkPvuvxPZGNmh0zGAlia9NM2ddmD6BsxF5Jpd82roXEITzeWL7ps15CHTYISCd846KMAkESw0YifZqroHMOZJSkgdjj1nb2MRYQ2EZbEdBO8H42spA4Dsjia0YRwRbyRGIuAlHsbreh2EbcfhnJPxYH/OkLQ5/n8kSJxFwE4tiZL2UbK43/B3EgiCOMJxJzEVLGIM5YyBegiUQDJHESiQZI4iQSDZDESSQaIImTSDRAEieRaIAkTiLRAEmcRKIBkjiJRAMkcRKJBvjXlpvureaJxFyELTc+suz3OUHgX8TxM0mTmOuI77bGwr+Ik0gkxkfOcRKJBkjiJBINkMRJJBogiZNINEASJ5FogCROItEASZxEogGSOIlEAyRxEokGSOIkEpNGKf8DrQAV0DiT0TMAAAAASUVORK5CYII=)
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. If the extension of the spring is
at time t, then the displacement of the right block at this instant is :
![](data:image/png;base64,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)
physics-General
physics-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. Then the displacement of the centre of mass at time t is :
![](data:image/png;base64,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)
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block pulling it away from the other as shown in figure. Then the displacement of the centre of mass at time t is :
![](data:image/png;base64,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)
physics-General
physics-
A tube closed at one end and containing air is excited. It produces the fundamental note of frequency 512 Hz. If the same tube is open at both the ends the fundamental frequency that can be produced is
A tube closed at one end and containing air is excited. It produces the fundamental note of frequency 512 Hz. If the same tube is open at both the ends the fundamental frequency that can be produced is
physics-General
physics-
When a block is placed on a wedge as shown in the figure, the block starts sliding down and the wedge also start sliding on ground. All surfaces are rough. The centre of mass of (wedge + block) system will move
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)
When a block is placed on a wedge as shown in the figure, the block starts sliding down and the wedge also start sliding on ground. All surfaces are rough. The centre of mass of (wedge + block) system will move
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m is given initial speed u as shown in the figure. It transfers to the fixed inclined plane without a jump, that is, its trajectory changes sharply from the horizontal line to the inclined line. All the surfaces are smooth and
Then the height to which the particle shall rise on the inclined plane (assume the length of the inclined plane to be very large)
![](data:image/png;base64,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)
A particle of mass m is given initial speed u as shown in the figure. It transfers to the fixed inclined plane without a jump, that is, its trajectory changes sharply from the horizontal line to the inclined line. All the surfaces are smooth and
Then the height to which the particle shall rise on the inclined plane (assume the length of the inclined plane to be very large)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAABqCAYAAABDL5YbAAAeZ0lEQVR4nO2deVDU9/3/H7uwC7vLAotyLCI3CrgIiKJoPBAQb7FGjYm1o6bp9Egy7Uynnf7RZqadHvlO2ukkTcf8E1OTTDUxRqOJikc8ghcg9yE3ct8u7LLLXr8//PGZbJvTJmHR9+Mfnaef+fD64Of5fr2P1/v9kblcLhcCgcBjkE91AAKBwB1hSoHAwxCmFAg8DGFKgcDDEKYUCDwMYUqBwMMQphQIPAxhSoHAw5gyU7pcLkZHR3n99de5dOkSFotlqkIRCDwK2VRW9DgcDvr6+lCpVPj7+yOXi8QtEEypKQUCwX/jPdUBfB42m426ujrGx8dJSUlBpVJNdUgCwXeCR5uypKSEgYEB4uPjhSkFjwwea0pfX1+WLFmC1WpFp9NNdTgCwXeGR48pbTYbLpcLpVI51aEIBN8ZHm3KL2JiYgKLxYK/v/9UhyIQfKNMyzWIoaEhrl69yqFDh7Db7VMdjkDwjTItTelwOLBYLIyOjk51KALBN8607b7a7XYsFgt+fn5THYpA8I0ybU35RUw+kkwmm+JIBIKvj8cuiTwoZrOZnp4ejEYjCQkJaDSaqQ5JIPhaPHSmNBqN3L59m4GBAfR6vTClYNrx0JlSpVIRHR1NcHCwqAISTEseyjGlQDCdeegy5RfhdDrp7+9HqVSi0WhEpZDAI5mW65QPyujoKH/5y184cuQI7e3tUx2OQPCZPFLdV4vFwvnz55k9ezYjIyMMDg4yY8YMVqxYMdWhCQQSj5QpnU4ng4ODqFQqKioq+PDDD6mrq2Px4sVs27aNWbNm4ePjM9VhCh5xvF544YUXpjqI7wqZTCaNJWUyGQ6Hg+HhYaqqqmhsbMRms6HVatFqtaLwQDBlPFKZ8j+ZmJigpaWFY8eOceHCBUJCQli2bBlLly4lNjYWrVY71SEKHkEeaVNOYrfbKS4u5sCBA9TX12MwGNi5cyfp6en4+/vj7f1ITVILphhhyv+Pw+FgbGyMjz76iEOHDlFfX8+OHTv48Y9/jF6vF8YUfGcIU34Kp9PJyMgIjY2NXL16lRMnTqDRaNixYwc5OTlERERMdYiCRwBhys/AarXS1dVFcXExly5doru7m9jYWHJycli+fLmopxV8qwhTfgF2u51bt25x7tw56uvrUalUZGRksGLFCuLi4sTyieBbQZjyKzA8PMyFCxc4deoUd+/eJTMzk9zcXJKTkwkKCkKhUEx1iIKHCGHKr8Hdu3c5fvw4//jHPwgLC+Opp55i9erVhIeH4+vrO9XhCR4ShCm/Bk6nE7PZTHd3N6+88goff/wxc+bM4Qc/+AHr1q3Dy8trqkMUPAQIU35NXC4Xdrud9vZ2bty4wcWLF2lvbyclJYX9+/cTExMjsqbgf0KY8n9gYGCAqqoqioqKKC8vx8vLi5ycHLKzs4mKihKZU/BACFP+jzgcDjo6Orh48SJnz57F6XSSkpJCVlYW8+fPZ+bMmVMdomCaIUz5DTFZR/v6669TXl6OXq8nJyeHJUuWEBERIRXBCwRfhjDlN4zD4aCwsJA33niDiooKVq1axc9+9jMiIiLQaDTiw7iCL0WY8lvAYrHQ1dXF5cuXOXToEP39/ezbt48tW7YQExMz1eEJPBxhym8Jm83G0NAQdXV1nDt3juLiYvR6PWvXriU3N5egoKCpDlHgoQhTfsvYbDYaGxu5cuUKJSUlmEwmEhISyMvLIyMjQ5TqCf4LYcrvCJPJxLVr1ygsLOTOnTvo9Xqys7PJyMgQFUECN4Qpv2O6u7u5cOECb775JhaLhQ0bNrBixQoSEhIIDAwUM7QCYcqpwOFwMDAwwKuvvsrhw4eJjo5mz549bNq0SczQCoQppwqHw8HIyAjl5eW89957lJeXExcXx09+8hNSU1PFWPMRRphyihkdHaWlpYXr16/zySef0N3dTU5ODps3byYuLu6RPcXdbrczPDyMTCaTqqJcLhd9fX0oFAoCAgIe2jLGR+qISU/Ex8eHkJAQZs2aRWBgIBaLhdraWhobGzGbzWi1WgICAqY6zO+cwcFBTp06RWNjI6mpqcD93sW//vUv+vr6iIyMfGh7E2Lw4gHIZDL0ej35+fk899xzLF26lM7OTk6cOMHRo0cpLi7GbDbjdDqnOtTvjNHRUS5dusSVK1ckzel0cvbsWW7cuIHFYpnC6L5dhCk9CKVSSWRkJD//+c95/vnnCQwM5NixY7z66qtcv36dnp4eJiYmpjpMwbeMMKWHsnTpUv74xz/yy1/+ku7ubr73ve/xz3/+k/b2dsQ0wMONOMzUg1Gr1axcuZLo6GguXbrEu+++S1lZGZs3b2bjxo3o9fqpDvE7xel0PhINkjClByOXy9FqtcydO5fAwEAiIyO5dOkSZ86coby8nPXr15Obm4tCoXhoiw5cLpdkxI6ODsxm8xRH9O0jTDkNUCgUREREEBISQmhoKJcvX6ayspLDhw/T2NhIdnY2sbGxD9V5tCqVCqVSSUtLCx988AFBQUFcv36drq4u0tPTpzq8bxWxJDKNmOy++fn54e3tTWtrK7dv32ZkZASn04lKpUKtVj8UFUFeXl60t7fT2tpKV1cXRqOR/v5+hoeHSUtLY+HChajV6qkO81tBmHKa4HA4aGxs5NKlS9TX1+Pn50dmZiZhYWF88MEHVFVV4XK5mDFjBr6+vtP+LFqFQkFoaCjBwcHYbDZ0Oh27d+9m1qxZzJ07l6ioqIe2sEJU9EwDnE4nRqOR/fv3U1BQwPLly6moqODIkSP8+te/BuDgwYOcP3+e8PBwnn32WfLy8qZ9xYvL5cLpdOJ0OpHJZHh5eUl/fxh6A5+HyJTTAKPRyIULFygtLSU3NxeDwYDFYqGlpYWbN2+ycuVKsrKyiI+PZ2BggMOHD1NdXY1erycwMHDafjFscHCQixcvcuDAAU6ePMmpU6cwmUzodDr8/f2nOrxvjen5v/WIYTKZKC0tRa1Wo9VqUSqVBAYGEhoaypEjR7Db7URHR6PRaAgLC5PqaP/85z+zcuVKVq9eTUJCwrc2Q+t0OhkbG6Ourk6qOlKpVAQHBxMeHv5A9+zu7uadd97h6NGjNDc343A4cLlclJWV0dbWxtatW5kzZ843+RgegzDlNGDypLyhoSFu3rzJvXv3GB4epqenh97eXux2OwBBQUFkZmYSEhLCzZs3uXXrFv39/XR1dbFs2TIyMzO/8T2bRqORuro6rl69SllZGU6nk7CwMDIzM5kxY8YD3/fcuXMcOXKE69ev43A4JL2vrw+r1YpGoyE2Nnba9gK+iIfviR5CJrd5DQ8P09DQgM1mY3x8nIGBAaxWq9uCut1uZ3R0lOHhYRYtWoRcLqeyspK2tjZ6e3tZtGgRUVFRqFSq/8mcDoeDrq4uSktLOXXqFO+//z4DAwPodDoWLlxIbGwsIyMjWK3Wr3XfyWc5evQo5eXlboaE+1m5oqKCy5cvs2vXrv/J+J6KMOU0QCaT4ePjQ2xsLNu3byc9PZ2enh5Onz7N+fPn3czV29tLYWEhzc3N/OY3vyEtLY2SkhLefPNN/vCHP7Bu3Tp27dpFYmKitLTyIIyPj3P8+HEOHjxISUkJMpkMb29vDAYD8fHxdHd3c/jw4Qe6t91up7KykrGxsc/8d6fTyejoKD09PcKUgqlBpVKRnJxMc3MzSqUSjUaDt7c3DoeDiIgIt+WPvr4+bt++zdq1a4mOjsbf35/ly5eTmJhIUVERf/3rXykqKmLnzp1s27btgY+8NBqN3L17l6GhIeB+w6FQKLBarXR2djI4OPjAz2u32xkfH0cmk31mWZ23tzdeXl5St/1hQ5hyGqBSqZg/fz4XL17EaDQik8kYHR2lu7ub1NRUt0O37HY7ZrOZsLAw6VR2hUJBSEgIq1evJioqitOnT/Pxxx9TUlLCxo0bKSgoQK1Wf63u7MyZM/nRj37EvHnzeO+99zh9+jRWq5Xa2lpmzZrFxo0bWbBgwQN1kV0uF7/4xS8YHh7+zC1aDocDpVJJWFjY1773dECYchqgVqvJzMwkIiKChoYGQkJCaGlpoaenhyeffNJtE7Svry8zZsygvb3dbTzn7e1NUFAQgYGBaLVaIiMjKS4u5sSJE1RXV7Np0yYMBgNarfYrxaRUKomJicHPz4/w8HBSU1MpLi7G6XQSGhqKXC7Hz8+PyMjIB3rmgoICBgYGKC0tdcuWcrmcOXPmkJmZiU6ne6B7ezpinXIa4OXlhb+/P3K5XPpGps1mY+bMmaxfvx6NRiNlJKvVSl9fH6dPn2b16tWEhIS4FRFMHq8RGxvLzJkzMRqN1NTU0NTUhNlsJiAggMDAwK8Ul0wmQ6PREBERQWJiIrNnz2bhwoXExcURFhaGTqd74FMTgoKCcDqdjIyMMDY2JpUPzpkzh4KCAjZv3kxERMQD3dvT+cJM6XK5KC8vZ2xsTGqtJv/8z27JdNY/3RJ7sh4cHMzQ0BBVVVUEBgZiMBgoKytzu35sbIyJiQnq6uq4cOECw8PD/zXT+unr09LSGBoa4p133uHWrVt0dnaSlZX1QHFOGnByZ0dLSwutra0P/Lzh4eEkJibS1dWFQqHAZDIRExNDREQEo6OjbqcSTN5nsqFIT0+ftjtnvrDMzmazsWXLFioqKpiYmMBms2GxWFAoFPj4+EgPPTlFr1QqUSqVUgnUZ+mTH101mUyo1Wpp29GkPjY2Js0KflVdo9H8130+7/7/qTudTum51Gq1dP9J3Wq1olKp3H6u1WplYmJCqjH9tG6z2fDx8flKusVikcZHn9YntycpFAq3bVkmkwm433WcjOc/9clJH4fDgdlsRi6Xu+mfd73L5WJsbAy5XI6Pj480K+tyuTCZTMhkMnx9faWs+3n6ZCb/LH18fBy4P0aefEe+THe5XG5F9na7XeqWf3ocbLPZmJiYwMvLiwULFlBYWDht63+/0JQul4uSkhKMRiMOh4Pi4mLeffdd1q9fz8KFC9FoNLhcLkpLSzl06BDbt28nLS0NjUYjrScdOHCA3bt3k5qaip+fH1arldu3b/Pyyy/z29/+lpiYGJRKJVarlfLycl566SV+97vfER8fj1KpZHx8nMrKSl588UV+//vfEx8fj0KhYHx8nJqaGv70pz/xwgsvMHfuXBQKBWazmZqaGv72t7/xq1/9iuTkZLy9vSX91Vdf5fnnn8dgMODl5cXIyAhFRUVcvHiRffv2kZSUBMC9e/e4cuUKN27cYOfOnRgMBuD+rOO5c+eorq6moKCAlJQU4H6GOnPmDM3NzeTn5zN//nzgvgFOnDhBV1cXOTk5pKWlAfc/AnTkyBFGRkZYsWKFpFutVl555RV0Oh3Lli1j7ty5wH2T/f3vfycoKIilS5dK1Swul4v/+7//Y+bMmTz22GOS7nQ6efHFFwkNDWX58uXEx8e7XT9jxgxWrVpFXFwccP9lf+mll5gxYwZ5eXlERUVJz/XSSy8RGRnJli1bpG+gjIyM8PLLLxMeHs7jjz8uZcmhoSEOHDhAUFAQu3btksrh+vv7OXjwIH5+fuzZs0faZtbb28vbb7+Nr68ve/fulSatOjo6OHr0KHK5nGeeeUY6JKuqqoqPP/4YjUbD3r17pXe1rKyMTz75BLVazXPPPSet0U5HvrD7KpPJSE5OxuFwSN2Q8PBw9u7di06nw9vbm+bmZpxOJzExMTz11FPMnDkTLy8vmpubsdvtJCQksHPnTkJDQ/H29qaiogKTycTatWtZu3YtM2fOlBa4R0ZG2LBhA2vXrpUmCyoqKujr62Pbtm3k5eWh1+uRy+VUV1fT0dHB9u3bycvLY/bs2chkMmpqajh58iQ7d+6UXi6ZTEZdXR3vv/8+O3bsYM2aNURFReFyuaisrKSsrIw9e/aQn5+PXq/H6XRSW1tLcXExu3btIj8/n/DwcBwOB3fu3OH69evs27ePNWvWoNfrcTgcNDU1cevWLZ5++mlycnIICwvDbrfT0tJCWVkZ+/fvJzc3F71ej81mo729nbq6Ovbu3UteXh6hoaGMj49TW1vLyMgITzzxBDk5OQQEBDA+Pk59fT3j4+Pk5eWRl5eHVqtlfHycqqoqnE4nOTk5rFu3Dq1Wi8Viobi4GB8fH7Kzs9m4cSMajQar1cqNGzekEw22bNmCRqNhYmKCy5cvo9PpWLVqFRs3bkStVmOz2Th8+DBxcXFkZ2dLG6qdTidvvPEGCQkJrFixgtWrV0uZ9fXXXycuLo6srCyys7Ml/bXXXiM2NpbFixezcuVKKYO+9tprxMTEsHjxYpYvXy4ZqbS0lNmzZ7N48WIee+wxaTxdWFjI7NmzWbduHYsXLwbuNyhnz54lLCyMLVu2YDAYpq0h4Suc0aNWq9FoNDQ0NNDR0UF+fj4xMTHodDo0Gg1NTU20tbWxadMmoqKiCAwMRK1W09LSQmNjIwUFBURHR6PT6fDy8qK1tZW2tjZ27drFrFmzCAgIQC6X09raSnNzM7t372b27NlSy3v37l1aW1v5/ve/T2RkpJs+ef3kepzT6ZSu3759OzExMfj7+0tfW25ra6OgoEDSzWYzTU1NAOTk5BAZGYlWq8VsNtPQ0IBCoWDFihVERUVJem1tLRqNhqysLEmfNIdOp5MqZibNUVpaSkhICBkZGURHR6PVaiVzzJo1i/T0dLfrCwsLSUlJITU1lfDwcLRaLTabjVOnTjF//nxSU1PR6/VotVrsdjvHjh0jJSWFtLQ09Ho9fn5+OJ1Ojh8/jsFgYMGCBYSFheHn5wfAyZMnSUpKYuHChZIul8v58MMPSUxMZNGiRYSGhkqmvHDhAgaDgSVLlhAUFIRKpcJqtXLlyhWSkpLIyspCp9OhVquxWCxcu3aNhIQEHnvsMUkfGxujtLSU2NhYli9fLr0jRqORqqoqoqOjWb58OQEBAWg0GulrZZGRkaxcuVLSm5ubGRgYIC4ujszMTLRaLVqtloaGBkZGRoiPjyczM3Pab/b+Ss1Jd3c31dXVOJ1O8vPzpX58Z2enVIScn58vtYodHR3U1dXhcDhYu3attO+tsbGRxsZGAgICWLZsmdQlaWhooKGhQeqafVqvq6sjNDSUJUuWoFKpJL2mpga9Xs+iRYukza4NDQ1UVFQQHR0tdaMBmpqauH37NvHx8aSkpEjd67q6Om7dukVOTg7R0dH4+vpK2bCoqIj8/HyioqLw9fXFbrdL+xm3bNlCVFQUPj4+2O12mpubuXjxIgUFBURGRqJUKrHZbDQ3N1NYWMjmzZuJjo6W9NbWVk6fPs3GjRuJjo6Wut1NTU1cvXqVDRs2EBkZiVwul/QrV66Qm5tLZGQkMpkMk8lEQ0MDRUVFrFq1ipiYGEmvr6/n9u3bLFu2TCoOmNQrKyvJzMyUuq0mk4nq6moaGxtJT0+Xurmjo6Ncu3aN0dFRUlJS3Lqzly5dYmJignnz5km6yWTiwoUL2Gw2kpKSJH18fJxz587hcrlITEyUdKvVyrlz55DJZNLMLdyv8z1z5gxyuZykpCQiIyNxuVxMTExw4sQJdDqd9Nl6l8uFzWbjgw8+IDAwkPT09IfiE4NfakqXy0VRURGDg4NSCRXcH7Ncu3aNoaEhFixYIHUTJ/W+vj4yMzOll2tiYoKioiKGh4fJz89Hq9Uik8mwWq1cv36d/v5+NmzYILXcFouFmzdv0tvbS0FBAb6+vshkMiwWCyUlJXR0dLBt2zZpZtFsNks7CHbu3OmmV1RU0NTUxJNPPilNDgwPD1NdXU1XVxc7duyQjD08PExtbS2dnZ3s3LlTyjBDQ0PU1NTQ1dXFE088IWXswcFB6urq6OrqYuvWrdLa2cDAADU1NfT29rJhwwapHKy/v5+amhqGhobIzc2VTv/u6OiguLgYf39/tzW4zs5Obt68SUhIiNtL19HRwdWrV4mMjCQtLY2goCBcLhednZ2cP3+euXPnMm/ePHQ6HS6Xi+7ubk6fPk1iYqKb3tPTw/Hjx0lJSSEpKYmAgACprvWdd94hOzubOXPmSA1WT08Pb7/9NitXrmTOnDkolUocDge9vb289dZbLFu2jKSkJJRKJXa7nb6+Pg4fPkxWVhbz5s3D29sbu91Of38/7733HgsXLmTevHlShU5/fz8nTpwgLS2N+fPnI5fLsdlsdHR0cPnyZQwGgzSOt9lstLW1cePGDZKSkqRx+XTnS005Pj7O2bNn8fX1Ze3atVKWHB8f5+LFi8jlctavXy9dPzlV7XQ62bRpk6R3dXVRXl6OUqkkLy9P0u/evUtVVRVKpZI1a9ZIektLC3V1dfj6+pKTkyPpTU1N1NfX4+vrS25urhTPnTt3aGhowN/fn1WrVklZu76+noaGBnQ6HcuXL5dm5IqLi2lra2PBggUkJCTg7e0tTWw1NzezePFiYmJiUCgUkt7Q0MCqVauk0rbJrUQ1NTXk5+dL4+ZJvby8nC1btrjplZWVFBcXs2PHDoKDg/H29sbpdFJVVcX169f54Q9/SEBAgNTA1dbWcvnyZX76059KhrTb7dy5c4cLFy7w7LPPSsa22+00NDRQWFjIM888I1W8TGbtDz/8kD179kjbqSYmJmhubpbG4JPZamxsjPr6em7evMmGDRuk9UCj0UhtbS1lZWVS1p7Ua2pqqK6uZuXKlVI2vHfvHmVlZbS3t7NkyRJJNxqNlJSU0NfXx8KFC92uLyoqwmQykZ6eTnR0NHC/QTx27BgREREYDAaCg4OB+w3oW2+9RUxMDPPmzXsosiR8iSmdTidnzpxBJpNhMBjcqjM++ugjvL29mT9/vtueuY8++kialv50GdT7778v1WF++myV48ePo1KpyM7OdisXO3HiBAqFgjVr1rhN2586dQqn08n69evdpu3PnDmD1Wply5YtbtP258+fZ3R0lK1bt0qDf7PZzJUrVzCZTGzbtk36mWazmWvXrjE8PMzjjz8u6aOjoxQXFzM4OMj27dsl/d69e9y+fZuBgQF27Ngh3X9wcJCKigoGBwfZsWOHFP/AwADV1dUMDQ3x+OOPS8872U3XarVkZ2e7ddPr6+uZMWMGS5cula6vr6+nurqaiIgIsrKypOvr6uqorKwkMTGR1NRUSb9z5w6lpaWkpKRgMBik3/+k8ZYtW8acOXMkfbIh2LVrF3q93q2BKywsZN++fej1eun33NjYyMmTJ9m/fz/h4eGS3tLSwrvvvsvevXuJiIiQ9La2Nv7973+zZ88eZs+eLS2VdXZ2cvDgQZ544gmpO2632+no6ODNN99k69atxMbGAkjZ86233mL9+vUkJCR81is8LfnSMjulUsnGjRtJTk52W/eZzJyJiYluOw3UajVr1qwhKSlJ0h0OB2FhYSQlJZGamiplN7vdzqxZs0hOTnark7RarURFRZGSksKiRYsk3WKxEB0dTXJysptuNpuJi4sjOTmZjIwMKRaTyURcXBzx8fEsWLBA0kdHR0lPT8fX19etIHt0dJS0tDQyMjKk1ntSn5xkmcwmk/c3GAwkJycTFhbmFs+8efOYO3euNIsM93sXSUlJxMXFSbPOcL/xMxgMLFq0yK06x+VyMXfuXDIyMtwaMrlczty5c8nMzJSMB/crfxISEli6dKnb2p6Xlxfx8fEsXboUrVYr6QqFQppZ/XR2VqlUGAwGsrKypGGGw+FArVaTmprqdr3D4UClUpGWlkZ+fj46nU4yk0qlYvHixWzatEnKYjabDV9fX7Kysli7dq3UrbfZbCgUClavXk1eXp6kW61WFAoFu3fvZtGiRdISi9VqxcvLi6effpqMjIyH6iSCL12nbGtrQ6PR4O/v7/ZBldbWVjQaDQEBAW4HGLW2tqJWqwkMDJR0p9NJa2srWq2WGTNmSC+Fw+Ggra0NPz8/t5d0shXUaDQEBwdLL+nExARdXV2oVCpCQkLcTNzb24uPjw+hoaFSLBaLhf7+fhQKhVvWNhqNjI6O4uPjI3X9JvWxsTGUSqWbfu/ePUwm02fqZrMZpVLptoVoZGQEs9mMj4+Pm/551w8ODmKxWNBqtW4v19DQEOPj4/j7+7vVpA4NDWEymaQ61k/rY2NjBAUFSWNhuN/Nu3fvHsHBwW4L7sPDw4yMjBAaGiqNwV0uF0NDQwwPDxMVFeVWTDEyMsLg4CCxsbHI5XI3fXJWdDIbOhwOjEYjfX19xMfHf6YeFxcnNdyT+0D7+vqIjY2VEsDExARGoxGj0cjs2bMl3Wq1YjQaMZlMzJo1a9oWCnwW4uAsgcDDmL4rrALBQ4owpUDgYQhTCgQehjClQOBhCFMKBB6GMKVA4GEIUwoEHoYwpUDgYQhTCgQehjClQOBhCFMKBB6GMKVA4GEIUwoEHoYwpUDgYQhTCgQehjClQOBhCFMKBB6GMKVA4GEIUwoEHoYwpUDgYQhTCgQehjClQOBhCFMKBB7G/wOrzgO1CbEE2wAAAABJRU5ErkJggg==)
physics-General
physics-
Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipe of radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitution is 1/2 and particle 'A' starts its journey at t = 0. The time at which second collision occurs is :
![](data:image/png;base64,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)
Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipe of radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitution is 1/2 and particle 'A' starts its journey at t = 0. The time at which second collision occurs is :
![](data:image/png;base64,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)
physics-General
physics-
AB is an L shaped obstacle fixed on a horizontal smooth table. A ball strikes it at A, gets deflected and restrikes it at B. If the velocity vector before collision is
and coefficient of restitution of each collision is 'e', then the velocity of ball after its second collision at B is
![](data:image/png;base64,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)
AB is an L shaped obstacle fixed on a horizontal smooth table. A ball strikes it at A, gets deflected and restrikes it at B. If the velocity vector before collision is
and coefficient of restitution of each collision is 'e', then the velocity of ball after its second collision at B is
![](data:image/png;base64,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)
physics-General
physics-
A 2 kg toy car can move along an x axis. Graph shows force
, acting on the car which begins at rest at time t = 0. The velocity of the car at t = 10 s is :
![](data:image/png;base64,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)
A 2 kg toy car can move along an x axis. Graph shows force
, acting on the car which begins at rest at time t = 0. The velocity of the car at t = 10 s is :
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two pieces? (
> 0)
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)
A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two pieces? (
> 0)
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)
physics-General
physics-
Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass m each and block 2 has mass M (M > m). Block 2 and block 3 are initially stationary, while block 1 is initially moving towards block 2 with speed v as shown. Assume that all collisions are headon and perfectly elastic. What value of
ensures that block 1 and block 3 have the same final speed?
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)
Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass m each and block 2 has mass M (M > m). Block 2 and block 3 are initially stationary, while block 1 is initially moving towards block 2 with speed v as shown. Assume that all collisions are headon and perfectly elastic. What value of
ensures that block 1 and block 3 have the same final speed?
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)
physics-General
physics-
A system of two blocks A and B are connected by an inextensible massless string as shown in the figure . The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass 'm' moving with a velocity 'u' hits the block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass 3m is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAAChCAYAAADtEqwhAAAgAElEQVR4nO2d6XNb13n/P9hXAiBIkFgIbiIpiotMWhJNMXJk2Y4Vt7ZTt5Ol0+nLdvqqL/qndKavOs540jap7U7itj87sWM5lmxL0UJxkURxA7gDJEjs+3bv74Vyb61IjC0KJCELnxmNxwB4cXDxxTnPec6zKERRFKlR4yEoD3sANaqXmjhq7EpNHDV2Rb0fFxVFkXK5TDKZJBwO09jYiM1mA6BYLJLL5UilUqhUKhoaGlCpVPLrC4UCABaLBb1eD0AikSCVSqHVajEYDJhMJgByuRw7OztotVrMZjM6nQ6VSgVAKBQim83S0NCAwWCQH08mkwQCARobG7Hb7SgUCgRBoFgssrOzgyiKOJ1O1Go1giBQKBRIp9MkEgkcDgdms1l+72w2Sz6fR6vVUl9fj0KhoFgskkwmKZVKKJVKLBYLWq0WgHg8TiaTQafTYTAYMBgM+3H7K8a+iKNcLhMMBtna2mJrawu1Wi2LIxwOs7q6SrFYxGazUV9fj1KpJJPJcPv2bfnLMRgM6HQ6yuUyS0tLLC8v09PTg9PpxGQyyV/mjRs3cLlcHDt2DK1WS7FYJJvNMjc3RzweZ2RkBL1ejyAIJBIJ1tfXmZmZYXBwELvdDtwT3+bmJpubm+j1ehobG1Gr1RSLRZaXl4nFYuTzeQwGgyyOzc1NlpeXMRqNNDU1UV9fjyiKJJNJJicn0el0eDwejEYjGo2GcrmMz+cjEAhw9OhRmpubq14c+7Ks5PN5rl+/zsWLF7l79y7RaFR+bn5+nv/6r/9ienqaSCSCIAiIosjOzg7vvfcen376KYVCAUEQKJfLZDIZPv/8c372s58RDAblGSCRSHD37l3+8z//k8nJSbRaLUqlkmQyyeLiIhcvXuTixYtkMhlUKhWlUon5+XmuXLnCF198wcbGBgqFAoDV1VU++ugjrl+/zsrKCqVSCYBUKsXvfvc7PvvsM9bX18lkMsC9mfHmzZv8x3/8B/Pz82SzWURRRBAENjY2+Pd//3e++OIL+bOVSiXS6TSffvop77zzDpFIBKWy+lf0io8wn88TDoe5desWoVCI/v5+GhsbKRaLhEIhlpeXWV5exmq14vF4UKlUBAIBZmdnyeVymEwmHA4HOp2OSCTC5cuXiUajeDwebDYbOp0OgFu3bnHr1i08Hg8ulwuNRgPA+vo6/+///T8EQaCvrw+TyYQgCGQyGa5fv47f72dwcBCn04kgCKTTaZaWlrh69Spms5muri40Gg2JRIK1tTUWFhbIZrMcO3YMq9VKJpPB7/ezsbFBNpvFbrfT0NCAQqFgeXmZ2dlZFAoFVquV+vp6NBoN29vbXLp0iXQ6jcfjwWq1yktNNVNxccTjcZaXl1ldXUWhUHD69GlcLhfZbJaFhQUCgQCiKNLW1kZ7eztKpZLFxUWmp6dpbGyks7OTpqYmNBoNW1tb/O53v0MURc6cOYPb7UatVpPL5ZiYmGB+fp7R0VH6+vpQKpXkcjlWVlb49NNPaWho4OzZs1gsFnK5HKFQiNu3bxOPx3nhhRfo6OigUCiwubnJ6uoqa2trtLa2Mjg4iFarJRQKMT8/Tzwex2q1MjQ0hN1uJ5FIMDExQTQaxel00t7ejsPhQBAEZmZmmJmZob29na6uLnnJ3NjY4Le//S0ajYbTp0/jcDieTnHcvXuXjz/+mI6ODkZHR9Hr9SiVSsLhMB9++CHpdJof/vCHeL1eRFEkn88zMzPD1NQUQ0NDDA0NIYoikUiE1dVVFhYWsFqtnD59GpvNRiwW486dO4TDYXQ6Hb29vbhcLvL5PLdu3ZK/5La2NpxOJxqNBr/fLwvm+PHjNDY2otfrSSQSfPLJJ0SjUV5//XXa2tpQq9WIosjU1BSfffYZzzzzDM899xwKhUK2pT766CMUCgWvv/46zc3NFItFEokEd+7cYWlpiZGREfr6+iiXy4TDYVZWVlhcXKShoYFTp05RV1dX6du+L1RMHMVikXA4zNLSEn6/n87OTvr7+9FqtUQiEZaXlwkGg9TV1TEyMkJDQ4N8Q3d2djAajXR2duJyuRAEgdnZWRYWFnA4HLS1teF2u9FqtQQCAS5cuIBKpaKvrw+Xy4VeryeVSnHz5k02NzcZHR2lo6MDnU5HLpfD7/czPj6O2+1maGgIk8lENpslEAhw9+5dRFHk7NmzOJ1Ocrkca2trrK6ukkgkOHr0KN3d3SgUCjY2NvD7/aTTaRwOBwMDA9TV1REOh7lx4wbJZFKe/RwOB8VikVu3brG0tITH46G9vV0W7JNAxcSRyWTw+XxsbGxQKBTo6OjgyJEjKJVKfD4fMzMz1NXV0draSmtrK0ajka2tLT7++GNEUWRkZASn04ler6dcLnP58mVmZmZ4+eWXGRwcRKlUIggCPp+Pd999l+bmZl5++WUsFgvFYpFoNMq1a9eIRCK89tprdHR0UCqVCIfD+P1+7t69S2dnJ8PDw7Id4Pf72d7epq6ujhMnTtDQ0EAsFuPGjRvE43HcbjdtbW04HA7gnp1z9+5durq66O7uxm63o9VqWVtb41e/+hUmk4nnn39e3u3kcjkuXrzI0tISb7zxBr29vSiVStkQrnYqtpVNp9PcuXOHfD5PZ2cnoVCIiYkJRFHkxo0bLC4uUl9fT6lUYmJiQv6iFxcXcbvd6HQ6fD4fq6urpFIptre3Zb/B6uoq4XCYeDyOz+fD6XRSLBZZW1sjEokQjUZZW1tDr9dTV1fH0tISm5ub8qwRDoc5evQosViM6elplErlfTOTRqNhamoKURQJBAJcv34dgKamJtbW1kilUgiCwPT0NMFgkM7OTpLJJOPj4xSLRWZmZtje3sblclEqlbh79y4AkUiEWCyGUqkkn8+zvLxMNBrFZDLJhmw1o6jUwZvf7+fnP/85oVAIlUqFxWJBp9MhiqJsI/T29lJfX49Wq6VcLrO5ucnU1BRHjhzhyJEjqFQq8vk8yWRSNmj7+/vR6XSUSiUikQjhcJhoNEpXVxdNTU0A7OzssLW1hSAIWK1WvF4vCoVC3omIoojZbKapqUl2oPl8PkKhEC6XC7vdjsViAWB7e5upqSlcLhft7e2yzVQul5mamiKdTvPMM89gNptRKpUUCgU2NjaYmZlhYGCAtrY2FAoFmUyGeDzO2toaOp2O/v5+1Go1er0et9tNX18fx48fr8St3zcqJo7l5WXeffddPvvsMyYmJlCpVPJePpPJUCqVZE+lUqlEFEWKxaLsMdTr9bK3slwuy55Sg8Egv75UKsn/9Hq9vHYXi0VKpRKiKKJSqeTtbrlcJp/PA6BSqVCr1bKfJJfLUSqV0Gg09z0ujUmr1aLT6VAoFCgUCkRRJJPJUC6XMZlM8vIgeVczmQxGo1F+b0EQKJVKFAoFlEolBoMBhUKBxWJhaGiIN954gx/96EeVuPX7RsWWFYvFwqlTpzAajRw9erRSl90zc3NzbG5uYjabcblcuN3uwx4ScE/sra2ttLe3H/ZQvpaKzRyiKMpeQkEQKnHJx+Kdd97h+vXrtLS0MDIywtjY2GEPCQCFQiHPOtXuJa3YzCFZ4F9dTg4TaRxKpRK1Wo1avS/HSHviqdutwP996Gr48JKtIP2rBsE+adTuWI1dqYmjxq7UxFFjV7614pB2TtIuqsajUz0m/CNSLpfJ5XJEo1Gi0SixWEwOw8vlcly+fFmOvIpGoywvL8uRXFIEWn19PVarFY1GUxVGdLXxxIlDmhEymQzb29vMz88zNzfH3Nwcfr+fYDBIJBKRRSIIAkajEZvNRkNDAy0tLXR3d3Ps2DF6e3vp6urCYrGgVqvlnU2Ne1TMCXYQSGF4t2/f5saNG/K5iTQjmM1m9Ho9Wq2Wqakp1tbW5LMWr9dLoVAgm82STCblIGCbzcbAwACjo6O0tLTIsa41npCZo1AokEqlWFlZYW5ujlu3brGwsEA8Hqe5uZn6+npaW1tpaWmhsbFRPkRTq9W4XC76+vro6+sjFosRCoVYXV1laWmJQCDA9vY22WyWXC5Hb28vnZ2dcuzI0+4beSLEkUwmmZ+f5+2338bv96PT6RgdHWVwcBCPx4PBYJAP0NRqNUql8r6AGp1OR319PRaLBY/Hw8DAAMVikXg8zuzsrBws7PV6GR0d5Sc/+QmNjY1PRCjfflLV4kin0wSDQX7/+99z48YNCoUCAwMDdHV10dXVRUtLCxaLRT5R/SpftR2USiUqlUp+nZQSYDabUavVmM1m3G43q6urzMzM8PbbbzM6Osrw8DBms/mJidyqNFUrjmKxyPb2NteuXePjjz/mzp07fP/732dsbIzh4eGKvIdOp6O1tRWv18vIyAgffPABly9f5le/+hXpdBqz2UxPTw9Wq/WpNFSrclEVRZGtrS2uX7/Oz372MwRB4Mc//jHnzp3jyJEjFX8/hUKBVqvlO9/5Dq+99hpDQ0PMz8/z1ltvsbi4KMeEPG1U3cxRLpfJZrNcv36da9euoVAo6O7uZnR0FLfbjdFo3Jf3VSqVOJ1OOQHqyy+/ZGVlhStXrqBUKnn22Wf35X2rmaoTR6FQIBaL8eGHHzI3N8drr73GqVOnOHLkyIFM7Y2Njbz00kuUSiWSySQfffQRhUKB4eHhp25pqbplxefz8ctf/hKlUsnw8DDDw8M4nc4D+2Kk4/2BgQG+973vYTQaWVtb48qVK4RCoQMZQ7VQNTOHIAjkcjkWFhb45JNP6Onp4fjx43R0dOzbUvKnaGlpQavVMjMzQywW48KFCxgMBhobG58a/0fVfEopint+fp7Z2Vk8Hg9DQ0NywO5Bo1AoMJvNjI2NYbVa+eUvf4nP56NYLD41B3lVI45sNsv09DQ7Ozuyl9Jmsx3qr1Sn08lZeJJ4V1dX5cj4bztVI45MJsPk5CTJZJKxsTFcLpd8GHZYqNVqmpqa8Hg8NDc3s7W1xfz8fE0cB00+n2d1dZVyuczg4GBVHYDV19czODhIKpXC5/PVxHGQlEolstks8XgclUpFR0eHXEHnUZFKThWLRQqFAvl8nmKx+Fjjq6+vZ2BgQM6gq4njAMnlcqTTaURRxGQy0djYuGdDVMo0k47m4/E4uVzuscZns9no6+sjm82ysrLy1IijKraymUyGZDIpx2TsxQgVRZFCocDs7CwXLlxgYmKC9fV1/H4/qVSKWCzGc889h8fjeeRrS3XCFAoF2WyWQqFAuVx+6IHft4mqEIdUrU+v1++5iJogCMTjcW7fvs0777xDNBoln8/LhWDC4TAul0uuGvQoSOEAUuJ0Op2mUChUfcG3x6UqlpVUKkUkEpG/zL1QLBbx+/34fD5SqZT86xYEgXA4zNzcHOvr68RisT2na2q1WhQKBTs7OySTyT1d40miKmaOQqFAIpEgEomQSqX2dA1RFEmlUqTTaUqlkhx5Dv+XOZ9Op8nlcnsWoJS1Xwk75kmgKmYO6SR2a2uLWCy25+vsVjVHypcFHsu7WSgUZJE9DUZpVcwcWq1WPj/Z65SvVqtpa2vD6/WiVqvRaDSoVCoUCgV1dXU0NzfjdrtpaGjYs9dVFEXZrX5Ybv2DpCrEodfr5Yo75XJ5T9dQqVQ0NTXR29vL6dOniUaj5HI5lEolTU1NdHV14fV65fd5FKTtcblcRqlUYjQan4r40qoQh9FolCPG9zpzKJVKTCYTJ0+epLW1lcXFRTY3N9FoNLS3t9Pb27vnEo9SBeJisYhSqbyvqtC3maoQh8FgwGKxyFtFqezSo9bUUCqVmM1meZnq6OhApVJhs9nkIvh7IZFIsLy8TDqdlpeqpyHwpyrEodPp5Dpb2WyWcDiM3W7fU8EVlUqFwWDYk7NrN+LxOHfv3iWVSh36YeBBUhW7Ffi/IN9kMsnMzAzxePywhyQTjUa5c+cOyWTyqcqrrRpxSGt5LBbj2rVrcu+Tw0TKyd3a2mJ2dpZ0Ol1V5aP2m6oSh8FgIBwO8/nnn7O1tXXo4iiXy8TjcdbX15mbmyOdTtdmjsNAEofZbMZkMrG2tnbogTWZTIarV68SjUZ55ZVXaGlpeWqEAVUkDoVCgUajoampib6+PoLBIJOTk8RisceOx9gLqVSKjY0NpqamyOfznD9/Ho/H89TsVKCKxCHR09PDT37yE2KxmFxUPpFIHPg4VldXuXbtGj6fD5PJxKuvvkpLS8uBj+MwqTpx1NfX09/fz/DwMFarlY8//piJiQkSiYTcXms/kToxXb16lZs3bzIwMMDY2JjcPeppoupMb6PRiNvt5vnnn6dQKPDee+/JrnGv17trVn0lKBQKbG1tcfPmTSYmJggGg/zN3/wNY2NjaDSapyZfRaLqxAH37I+enh4KhQI7Ozusrq7y1ltv8cYbbzAwMEBzc3PF31NqAHT9+nUuXLhAR0cH3/ve9xgYGKiqYOeDpGrFUV9fz9GjR3n55Zf5/PPPmZmZYXx8nGQyybFjx2hqapJd7ns1EKW+sZFIhEAgwM2bN1leXqapqYmTJ09y9uxZuRfMYW+rD4OqFIeEw+HglVdeweVy8cUXX/Duu+8yMTHB2NgYZ86cobe3V257sRfK5TKJRILJyUk+/fRTVlZW8Hq9/MM//APHjh2jubn5qdmZPIyqFodCoZDjNFQqFWazGZ/PRzAY5P3338disdDR0YHb7aa5uZnGxkaMRuNDbRKpv0sikWBra4tgMEggEGB5eZlSqSTPFkePHuXYsWNyZ8eDJJ/PE4vFmJ+fx2Qy0dPTw+LiIsFgkHw+T2trKx0dHbKzcG5ujmQyiVKpxOPxyMlXlaKqxSFht9vlPrSTk5N88sknzM7OsrS0RCwWY3NzE6fTicPhkNuDSwbkV5v4ZLNZ+fWBQIDNzU22t7dpa2tjcHCQsbExjhw5cmhe0Hw+z9bWFp999hkGg4F8Ps/09DRLS0skk0m6urrkQ8mtrS3Gx8fZ2dlBEAS5OlFdXd19bdsfhydCHHDPg2q1Wjl58iTd3d34/X78fj/Ly8usra1x/fp1otEogiBgNptpbGzEZDKRy+VIJpMkEgmy2Sw6nY6mpiZaWlo4ceIER48epa2tDZfLRV1d3aG6x3O5HFtbW1y8eJFwOMz4+LjcNn1nZ4fp6Wn++7//m5aWFgwGA6VSiXg8TiQS4be//S07Ozu4XC48Hs+ek8K+yhMjDmmJsVqtWK1WzGYzTqeT1tZWgsEgW1tbcjoC3As9lKr0SFHoCoVCTppyOp1yO0+bzfbYaQZSqapIJEKhUJCbEdrt9m98bUEQ5I7euVwOq9VKV1cXVquVeDzOxYsXGR8fx2g0MjAwQF9fH/l8Hr/fz/vvv08gEMDv98v353F5YsTxx9jtdux2O729vfJjUqByIpGQS11LAUBWq5W6ujq5l1wlKZVK5HI5ZmZmmJ2dJZPJYLPZaGlpYWBgAKfT+cinuS6Xi3PnzvHcc8/h9XrJ5/OkUimuX7+Ow+FgZGSEN998E6VSyeTkJHfu3KFUKrG0tFSxNmpPrDgehnTsLxmvUjyqWq2WI8v2Y8nw+Xx88sknXL58mYWFBbm0pdls5gc/+AFnzpyhr6/vkQRit9s5fvy4bBjrdDr5YNLr9co7KelMSrK1Krnl/laJQ1p61Gr1gWWjlctl1tbW+PDDD5meniYQCMitUTUajVyAv6en55HEYTKZ5AK8CoVC7m6p0+mw2WzU1dXJQpfEI7Var5RAni5/cIWRtseSy317e1u2G0qlEsVikenpaW7fvv3IUfVSC9TDdNl/q2aOw6JcLpNKpeTQAumXKyV3FwqFPf2aDzs8oDZzPCbSlG61WuVTW+lLlTpzf3UJeJKoieMxkIzBtrY2XnvtNblVuVRnXafTMTY2xujo6BOZ51JbVh4ThUKB1+vl9ddfl3Nyl5eXaWlp4dSpU5w7d47e3t5v5LFUqVQYjUY8Hg8Oh+OB561WKy0tLVit1vsy7rRaLQ6HQ56pKiXEmjgqgHSuIeXnvvfee5w6dYp/+qd/kp1s3wSNRoPVaqW/v5/29vYHliKn0yn7Tb5am1Wv19PR0SGnflYqKKkmjsdEas8uue0bGhrkrXRDQwNwL4jom7jljUYj7e3t/PjHP8ZsNsvZdRJDQ0M4nU6cTic2m01+zm638+KLL8pJ3lartSKfrSaOChCJRORznng8TqlUIhaLsbi4iNFoxOFwyCfLfwqtVktDQ4Msqj+mpaXloXGsRqOxYl7Rr1ITx2OiUCiYnZ3lX/7lX4jH42xvb5NMJhkfH+ef//mf8Xg8cseHJ62GWG238phIh3kej0fuQ1coFAiFQszMzMhdoJ7E+NMnb8RViMPh4MyZM5jNZqLR6H2lLru7uzl69KjsMf3jEhNfrZm619ok+0VNHBWgsbGRkZERWltbMRqNKJVKHA4HAwMDtLW1oVarmZ+fJxgMkslkZBGIokgikWBzc5Pl5eXHKnm1H9TEUQEMBgMul4uuri46OzvR6/W0tLQwNjaG2+0mEonw61//mqmpKXlmgXs7nUAgwPT0NF988QVra2uH/EnupyaOCiB5RXt7ezlx4gRGo5EjR47wyiuv0NzcjN/v56c//SmXLl1ic3NTzv8VBAGfz8fnn3/O+++/z9zc3CF/kvup7VYqiFQfPRQKMTg4yJEjRzCbzXI99ocdvknt13d7/jCpiaOCeL1eRFEkGAzKqQ1PMjVxVBC1Wo3H4+FHP/rRobQeqzQ1cVQQhUKBTqfD5XI90hF9tS0nEjVxVBjJOH0YDwvhk85lqpHabuUA+WNxSH6OeDxelQKpzRwHgBSNvrOzw+LiIna7XU60WlhYYGNjo+q8o1ATx4EghRLOz8/Lx/k6nY719XV+//vfs7y8jNfrPexhPkBNHAdAS0sLf/VXf8WtW7eYn5/nF7/4BQ0NDVgsFrxeLzabDUEQqq6eek0cB4Db7ea1115Do9Fw5coVtra2gHtnMs8++yxKpZLNzU3sdvshj/R+auI4ACwWC729vTQ1NfGDH/yAcrmMVqvFYDDI3Z8KhULVVRCqieMAUKvV1NXV7blrw2FR28rW2JWaOGrsSk0cNXalJo4au1ITR41dqYmjxq7UxFFjV546P0ckEmF+fp5MJvNIrTpEUWR5eZlQKMTVq1cJBoPfyG8hVfdpaWmRa5I9KTx14lhZWeHnP/856+vrj9SPXhRFFhYWyGQy/OIXv8BkMn1tNruUuzo4OMif//mf09HRURNHNRONRhkfH6e3t5fnn3/+kf42EolQKpWwWq3fqItCoVBgenqaaDRKMpk8lKZCj8NTJ45MJsPS0hJjY2OcPXv2kf62WCwiiqJclfDrQgFTqRRLS0vkcjlyudyB9IupJE+dOKTW4w6H474apt8UqZ/9NyGZTGK324nH409k2aenThyA/Ovf7wjxYrH4jWqfFgoFUqkUmUxGrsD8VTQaDWazGaPReKA2y1Mpjt2QEp0lW0IqJfnV+qYKhUKefb76nFScZS8zRDabZW1tjUAgQCQSecCW0ev1NDU1ycX/jUbjgfS3rYnjDwiCwMrKCqlUSt6iSvaJlI/i9Xoxm83E43GWlpZYWVmRn+vv75cLxT4qkUiEK1eucPXqVRYWFjAYDPJ18vk85XJZ7l518uRJzp8/T2tr674vVTVx/AFBEJifn8fv92M2mykUCiSTSUKhEOVyGZPJxLPPPovdbmd1dZWNjQ22trbIZDJ4PB5isRj9/f14PJ5Hfu9cLkcgEGB9fZ2dnR2Ghoaor68H7i05mUyGWCyG3+8nEonQ1tZGXV0d9fX1+yqQmjj+gCAITE9Pc+nSJURRJBqNkk6ncTgcRKNR5ubmeOmll3A4HExOTmI0GrFYLMzNzaHT6Zienubv//7v9yQOicbGRtxuN//4j//IsWPH5MdTqRSrq6v89Kc/5YMPPuDkyZM0NzfLAtovauL4A1KyczabJZfLceLECZ599lmsViuzs7P85je/IRKJoFKp+OEPfyj3PJmYmOD27dtMTU2xvb39WGOQUhj0ev19xrJGo0GtVuN2uzGbzSSTSWKx2CPtnPZCTRx/hJRGcOLECf76r/8anU7HtWvXCIVCjI+PA/Bnf/ZndHd3o1AocLvd5PN5Pv7440fyuD4MQRAoFouk02n5WlIGvrTz2a1N2X5QE8cfYbFY8Hg8tLS0yM0FDQaD3Ne2sbGR+vp69Ho9pVJJbjFWiW4F0pbW5/PJGXBSp6mdnR1mZmYQBIHOzs6H1imtNDVx/BFSuUeTySRvKaXZRK/Xo9frZde5VN66UhWDk8kkgUCAjz76iMbGRuDeNjeVShGLxUilUrS0tODxePbdGIWaOB5AaujzsC2p5MfYry9FqkaYSCTkBCep60I2m+Xo0aMMDg5isVhqfo6njaamJkZHR3nzzTdpbW0F7tkc2WyWcDjM5OQkt2/f5n//939JJBK89NJL+1rCsiaOKsJkMmG32zl79iz9/f3y47lcjmg0iiiKrKysMDMzg9Pp5MUXX9zX8dQiwZ4ApHanAwMDnDp1ilKpRDgc3veiL7WZ4w9IHQe8Xq98fiGh1+tpbGykpaUFm80mr/cKhQKtVktjYyP9/f37nuuaTCbZ2tqiXC7XbI6DRKFQ0NbWhlarxe12Y7FY5OdMJhOtra3odDpMJpNsLErb3La2Nl544QXcbvdjjaFYLFIqlR4IQSyXyxQKBebm5lhaWqK+vh673V7brRwUKpWKEydOUCgU0Gq1mEwm+bmGhgaGh4cpFApywxz4vy7ZJ06coK2tjaampscaQzQaZX19nbfeeuu+WahQKBCLxVhZWSGdTvPCCy/w7LPP1sSxH4iiSCAQYHJyck9/v7Gx8dDHl5eX7/v/dDpNLBb72pJOBoOB1tZWtre35bCATCYDIIcIaDQaent7aWho4PTp03R0dNTEsR8olUpmZ2f59a9/va/vUygUCAaDcv+U3b5Mq9XK8ePHsVqthEKhB8aq1+ux2Wy0trbS2tr6QBuv/aIi4pB8/1KM5fvNU0EAAAkUSURBVKNa0alUSm69mcvliMfjex6L5KTS6XQPvYFOp5Pz589TV1dHLpfb8/t8E0RRpLW1FbfbTVNT066NkE0mE52dnTQ1NT0wJqk6obTUmUymAzFGoULiiEQihEIhua73o4ojk8mwvr5OJBJhbW2NL7/8cs9jkW5kT0/PQ4/PnU4nr776Krlcbt+3gtJuprm5mebm5l3FIe14JJd5taAQK3CHLl++zBdffMGlS5eIRqOPXBlPOo2Mx+NotdrHqnBjNBqx2+383d/9HefPn3/g+WKxSCaTqWhb7z+FdAyv0+lQqVRPVFOeiswc+XyefD6PTqfj+PHjdHd3P9Lff7WDM7CnGyiKIvl8nqWlJa5evUo0Gn3o66QOjDW+nootXgaDgfb2ds6ePcsbb7xRqct+YwRBIJVK8f777/PRRx+RzWYPfAzfNp6cOa7GgfPQmSObzbK0tES5XMZisdDQ0IDZbH7ki0uevUQiQTqdRhAEjEYjNpsNrVZ7YFZ3jb3xwLcjiiLxeJzf/OY3ZLNZuru7ee655/YkDsnInJ2dZXV1lUKhQGtrK319fdjt9po4qpwHvp3t7W1mZma4evUqoVCIO3fu4HK5HilPolwuyzGXH3zwAZlMhlKphCiKsvv51Vdf5cSJE09kv9WnhQfEEQgEuH37NqFQSM7CWltbI5VK3Rc696coFovMzs7y5ZdfcuHCBTweD06nE5VKRSAQIBgMYrFY5G7NNXFUJw+Iw+fzcevWLbq7u7FYLPj9foLBICsrK3R3d6PT6b72otlslkuXLrGwsMDo6Cjf//73OXXqFAqFgsnJSS5dusTy8jJffvklo6OjT1TNiqcJWRylUolcLofP52NxcZHz58/j9XrR6XRsbW1x+/Zt+dj669BoNHLzO5fLxcmTJ+nq6gLueVMbGhpYXFwkEonIDrBIJMKNGzcwGAx0dXUxNzfH5uYmxWIRr9dLW1sbFouFnZ0dZmdnSaVSiKJIQ0MDPT09dHV1VW3HoycVWRyFQoGdnR1WVlYIBoO0t7dTX1+PwWDg7t27TE9Pc+7cOerq6r7W9tDr9Zw7d45SqYTZbEav18uxCtlslkKhgFKplA3SQqHA+vo6//Zv/4bVauX111/ngw8+YGpqilQqxXPPPceZM2fwer34fD7+53/+h2AwSKlUoq2tjb/8y7/E7XZXZc+SJxlZHOFwmCtXrpBKpWhra8Pr9eL1eqmrq2NycpL5+Xm2t7epq6v72tIFKpUKu90ulzoIBoOsra0xPz/P5OQkd+7cYXh4mDNnzqDT6eRZKxgMMj8/T6lUoqmpiXPnzrG5ucnGxgb/+q//itfrxel0Mjo6SiqVIhAIMDExwdWrV/F4PHR0dOz7DXuaUMK97Ws4HOby5cvk83l6enqor6+noaGB9vZ2TCYT6XQan89HOBz+2otKEVJGoxGtVksikcDv93Pnzh1mZ2dZWVlBqVTKs5AoipRKJZLJpOyG7+vr4+zZs7z44ovo9Xpu377N5uYmZrOZsbExXnzxRU6dOoVWqyUUCrGwsEA6nd73G/Y0oYZ7ruft7W0uX75Md3c3g4ODaDQayuUyer0er9dLPB7n5s2bNDQ0PHJXoUwmQyqVQqlUolQqKRaL+Hw+fD4fIyMj9722p6eHv/3bv6Wjo4P6+npKpRKzs7PcuHGDkZERzp07x9jYGHAv8fjmzZsIgkA4HJY7PdeoDGpBEFhdXWVhYYFQKCRHL129ehWj0YgoikxNTRGLxdjZ2aG7u5uxsbFHSu6RDNmBgQGGhoZYXFxkYmKC8fFxhoeHcTgc8mstFgsdHR1YrVY5JkP6r91ux2azyUaxlHCcy+UQBKFmkFYYdblcZnFxkYWFBeBeaNvS0hJLS0v3vbBcLsuezmQy+SeDTgRBkI/F9Xo9zc3NuFwu4F4E9fr6OjMzM/j9fnw+333phFKkt+T7UCgUKJVKNBqN3BtNQqqq8yQdgz9JqEulErdu3WJtbY2hoSFGRkYYGhq670WCIDAzM8Pbb7/NxsYGd+/epbe3d9e4i3w+z507dyiVSnR2dmKz2eRAF6PRKJcwks5dvhr9JEU+PYkF1r5tqMPhMPPz80SjUb773e9y5swZnnnmmfteJAgCZrOZK1eukE6nGR8fx+Vy7SqOQqHAjRs35AixoaEhOStcyiRPpVLyVler1cqF0vYzF7XGo6FeX1/H7/eTy+U4efIkPT09D03OaW1tZWRkhLm5Oa5evcp3vvOdXc9bisUiExMTzM7Osra2JjvDlEolkUgEv9/PxsYGgiDIOSKPW9uiRuVRf/755+RyOVwuF0eOHNm1lJDNZmNkZISVlRUmJyfZ2Nigs7PzvuQfCb1ez3e/+11KpRKXL18mGo1y4cIF9Ho929vbrK6uotVqGR4eprOzE71ev2u4f43DQy0IAseOHaO9vR2n07lrEKzZbObYsWP09vays7ODWq3etSKvVqvlxIkTpNNpNjY2SCQSzMzMYDAYSKfTpNNpzpw5w9jYGE1NTXJBtq6urodmjTkcDrq7u2loaLjvHEan0+FyucjlcjQ1NX0j136Nb476/PnzCIKAxWLBZDLtut7r9XpcLhd/8Rd/wejoqHzu8jA0Gg3d3d3U19czNDTEysoK29vbCIKAzWbD6XTS3d1Nc3MzOp2OYrGIy+XizTffxOl0PnC9oaEh9Ho9/f3999k5NpuN06dPUyqVMBqNtdjQCqNua2uTQ+j/VPCNtG2UDFG9Xr9rYs1XE4ylkkmpVEqOBLNarfI14F5rTZvNxqlTpx46c7W3t2O1WrHb7felKRqNRvnATaVS1Y7+K4z6UcsVGo3Gb1wWWqvVotVqv7YkolKplJeVh+FwOO5zlEnodDp5GZICjGtUjpr3qMauVCyIs1wuk06nWV9fZ3p6ulKX/cZIXtlgMIhGo6ktMRWgYuIoFouEw2EmJiZ2TSjaT0RRpFAosLKygsFgqFiFv6eZiojD4XBw5MgR0un0gaUZPgyVSiWXYXzUk+MaD1IxcfT09KBSqQ4900zKRm9paTnUcXwbqEgitVR+IZ/PH/qxuXSKazAYDqSGxbeZioijxreT2la2xq7UxFFjV2riqLEr/x9NgiObhk1V1gAAAABJRU5ErkJggg==)
A system of two blocks A and B are connected by an inextensible massless string as shown in the figure . The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass 'm' moving with a velocity 'u' hits the block 'B' and gets embedded into it. The impulse imparted by tension force to the block of mass 3m is :
![](data:image/png;base64,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)
physics-General
physics-
A sound source is falling under gravity. At some time t=0, the detector lies vertically hallow sources at a depth
as shown in figure. If v is the velocity of sound and
is frequency recorded after t=2s is
![](data:image/png;base64,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)
A sound source is falling under gravity. At some time t=0, the detector lies vertically hallow sources at a depth
as shown in figure. If v is the velocity of sound and
is frequency recorded after t=2s is
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)
physics-General
physics-
A gun is firing 20 balls per seconds of mass 20 gm each on the smooth horizontal table surface ABCD. If the collision is perfectly elastic and balls are striking at the centre of table with a speed 5 m/sec at an angle of
with the vertical just before collision, then force exerted by one of the leg on ground is (assume total weight of the table is 0.2 kg and g = 10
)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAACSCAYAAABfVZ8qAAAgAElEQVR4nO3dd3gU1f7H8ffWZJNNJ4VqQg2gFClCQAFFigJSBPGKiCigVBFUOqgIxCsqIj9KpAtSlCLlikAg9F5DSQKRmpC6ySbZbJ/fH7kXiQlqMNlNOa/n8VFnZme+OyQfzsycOUcmSZKEIAjC3yR3dgGCIJQtIjQEQSgSERqCIBSJCA1BEIpEhIYgCEUiQkMQhCIRoSEIQpGI0BAEoUhEaAiCUCQiNARBKBIRGoIgFIkIDUEQikSEhiAIRfLQ0LBYLKSlpWG1Wh1ZjyAIpVyB0EhISGDQoEH4+PhQq1Yt/Pz8GDVqFJmZmc6oTxCEUiZfaNy8eZMWLVrg4eHBiRMnOHPmDLNmzeHcuQs0atSIhIQEZ9UpCEIpIXtwEJ4XX3yRRo0aMWXKFJRKJRkZGZw6dY7fflPw/fef8Ntv13jqqWcZOLAnL774IhqNxpm1C4LgBPdbGjdv3uTYsWO8/fbb+TYwGnMxmTR07DiKjIwsoqK68uaba/Dze4wuXfqzadMmjEbj3z7g9u3biY+PL75vIAiCQyn/9x83btygVq1aWK1W9Ho9Bw4c4N///jfR0dGADF/fADw9tUjSOLKzs7HZbJw6dYODBxcB79Ku3bMMGdKPrl274urqWujBEhMTGTRoNGazgtDQYMaPH0LPnj1Rq9UO+rqCIPxT91salSpVIjExEbPZzPLly3n//fcZNWoU165d48iRswwb9jYajYrmzVtx+vQ1Vq06Q6dOHZGk46hU1Tl4cB+DB79L5crV6dKlH1u3bsVkMuU72KuvDiUzcxRZWTGcPPkBQ4ZsxN8/hBEjxhMTE+PwLy8IQtHdD42GDRvi7e3NDz/8QHh4OJs2beK1115DLldw/fp1rl2LY926TcTFXeTIkR14eHhx44ad2rWDUShu8N13axkz5htq1mzOoUOHeO21Rfj5PUaPHgP4+eefiYhYyunTGVitY/572E7o9RvR68+xeHEQLVq8RKNGz7Bq1eoiXe4IguBY+W6EHj58mE6dOvHcc8/xzTff4OnpiV6v59Kly7i7uyOXK9i8+ScuXoxm+PBwDIYrBAZWYdSoEbz33jRatWrKqVNGNmyYx/Hj19DrdwJbcHNbhEKRSlbWYGAAUOUh5RxAq41AJtvLyy/34Z13XqdFixbIZDJHnAtBEP6GfI9c27Rpw9NPP01gYCCXLl3i7NmzXLhwgczMDGw2JRkZJuRyDefOXeT8+R34+vphtVqpXbsWcXHxWCwKoqO1VKs2CoslDjiNVvslNWqk0a7d4zz55H5cXBqgVn/6kHKeITt7NVlZl1ixojavvfZeyZ8BQRCKRPnHBU2bNiUlJQUvLy/sdjupqelIkp1Ll6JZvnwxSUn3qFevFmvXrmLp0sW89dZQ7t1LJixMy+3bEvXr68nI0FO16mMkJg6ib98eTJ48CUmycvNmNqdO/cZXX40kI0PCZJr2kLJ8kKQxJCev5OLFizRq1KiET4MgCH9XgdDo27cvXbt2xWQyERMTg8FgwMvLnytXzjNlylReeOEFVCoXUlKSOHToEDNnzgQkAgLCyMgwYDAYMRpNpKXdpUmTYKZNm4S7uw9ZWSY0Giu5ubV45pmF/PRTH+ADYAseHutRKNKw20PQ68cCTQEwGp9j7959IjQEoRQp0I3carViNpvR6/UMHDiQAQMG4OnphtlsRqNxJTj4MRQKNTk5ZgIDK9Op0/MoFCoMBhkZGTkYjTmkpt4kMzOZ1q2fJjfXRnq6BbChVFqoVs1A8+ZKfH39cXUdSP36s/jggw5MnvwWXboEoNF0RKlcC4DZ/Cxbtuxz9DkRBOFP5GtpGI1G+vXrx6xZs+jZsye5ubkYjUYqVarEs8+2Z9KkSYSGNsDHx5fs7ExMplw6duzKwYNHiIs7SUDAY6SkJLJuXTjwJAkJFlJTs1CprIAFkykXszkXq9WCwZBJtWoX+P77Pfj5eZGZmUNAQBtCQprx9dfDsVrbAs9w9eqHREVF0a5dO6ecIEEQ8ssXGuvXr6dGjRr07t0bHx8fzGYzt27dxsfHF2/verRo0Z4FCzbQt+8bmEze5Oa6kJ19HldXNbt2rUahUHH9+hmUyprY7S3Zt28vbdu+ikplAewYjUaMxlzi4+OQycyMGTMdd3dftFoVkEtqqgu3bj1FtWrduXFjCTbbDJKTX6Bz5/5UqqTls8+m8PrrryOXizf6BcFZ8v32nTx5kpYtW2K32/nxxx8ZOnQo48ePY+PGjeh0N6lfvy5xcefQ65VkZCgwGuXodHVJSkonLq4NV6+2Q6Xy4733XqJatd2kpGQQETGdlJRkdLo09PoMLl+OZt26TzCZzDz2WH3M5izMZh3JyUb8/XNo2TKJJ56oglJ5DA+PhjRsuIs2bdrg5xfAO+8MJzDwMf7v/xaKvhyC4CT5WhpqtZrs7Gx69OiB1Wqlf//+KBQKDh8+yvvvv0vbtu2RJNDrM8nNtWIwmDh+/CdksgbA03h6Dmf9+gi6dOnChx+OpX377kRHR3P58itUrlwXg0FPevpdrNZ5qNUfcPlyInq9FldXGTk5FszmLDIzLeh0d1AoTvHhhzPo1esNJMnEzZtZHDhwlgUL3mH8+B+YOPET3ntvOGPGjMDX19dJp08QKp58nbs2btzIyJEj6d69O19//TV2u52UlFTu3k3n9OlDTJkymXr1nqFLlxEYDHpOndrKiRN7kaTB+PtvJTJyK6Ghofd3npWVRYsW7YiJaQS8BHgCYYAGhWIIrVsbePXVvB6idruFjAwTubmZfPXVIHr37s6kSd9Qp4476ekGrl9PY/DgSuh0G0lJWY4kLUWj+QLYxOuvv8bEie8THBzs4NMnCBVPvpZGlSpVsNvtjB8/HpvNht1ux263I0kSQUE16NDhWQ4fPsrcuW9gs+Uil3dGoXiGxx8/xa5dR/P9jW8wGGjbtjM3b9YH5gFe+Q5ss33KsWOtcXHR0qZNb2Qy0OuT2Lx5AaDkiSdewG43kpUlw2o1YrXaGDHiOhkZ1Zg+/RgaTRQ+PrtJTNSxcuVSNmxYS4sWbQkPn07Tpk0dcOoEoWLKFxpRUVF069aNhIQETCYTSqWS1NRUEhNT0OnSadDgJXbvPorZHA2Y0Gj+Re/ejVm6dANKZf4uH0OGjCE2th5G4zKgsG7gQVitkezf/yZRUS/j4uKB0ahHkgahUpnIyLBy924W2dkGrFYbN2/mYrUasVisuLlpqFLlSz7++CvCwp7k0qW7LFmylN27txAW1o0mTRrw8ccf0KlTp5I7c4JQQeX7TbdarSgUCoKCgsjOziY9PZ3k5BQyM13Iza2D3X4XSbIASbi79+aTT95n7NiRBXYaFxfH5s3bMRqvUXhg/E8INtt+QIfVmk7eOykaTKbRREXtonr1Bri4yDGbJUymXAwGAwcPbkCjcSUiYiNVqoSQlaWgbl0Fo0ePwWiEw4eTOHasP336fEBg4Ed8/PF4XnnllQKhJgjCo8n39CQsLIyoqCj0ej1KpRJPT09MJivZ2QpycoxERx9EqayFp2c3Nm9eXGhgAKxcuRardQjg/heHt/z33z5ALeB/I4FN5tSpvezatYrUVB1ZWelkZuqJjT3FkSM/0qNHDzw8vArs7dln/0Vu7l6gHipVbVJTUxkxYgzVqj3G1KnTycnJKcKpEQShMPluhAK0bNmShg0b8vrrryNJEjEx17h3z5O7d5NZu3YqWq0Phw/vpm7dug/d6RNPPEN09HygcSFrLcA61MrpaOTJWJCTa+mPJM0BHnwKEodS2QeNJhl//5pkZ2eg06UikzWhb9/mjBw5AC8vLVqtjIQEA9ev53DvXiYTJ/bAzU3FO++8R7t2bUhJyWXDhk3s3bsRUDFq1HDGjRtNQEBAMZw+Qah4CoRGQkICXbp0QaPR0L59e9LSMrhw4Q7nzkVSo0YtTp48iI+Pz5/u1MenBhkZvwGKP6yJx03ejlruWfSuHIivSoXBZuOQLpO9KZkY7WuAng9sv5tq1caQlHQb6ITFMhv4iVatTvH225OpUwfsdjm3b9v/+4TlKkuXvse33y6hc+du6PUK7HYdd+9msHz5JrZuXYrN9iIy2Xr69XuZKVPGU6dOnWI4jYJQcRQIDQCz2czKlSvZsmULp0+fJT09l+7dX2T9+hV/696At3d1MjPjgPzD/rnJezK21mUmFfKLeiojg07HLmKy6x+sBDe3EA4e3Mb3329gyZKl2O2tsVqjGD16LlWr5j3etVrN5OQY+b//G0uVKt5s3LgRo7ESCoUcszkDvT6V//zHwnffvUpq6mJAj5fXFyiVsQQFVeaLL2bRpUuXIp04QaioCu2PrVarGTJkCDt27KB79x5MnfoRP/30/d++mejh4QMYCiy3sY2r2dmYbLYC6y5lZaEgB3hwciY1ktSf06dP8+WXc7h37zdmznwWNzdX5s8fza5dy7h06QynTx9k5crppKeb8PevR1ZWLlZrJmZzBkqlnuvX7Xh75xAQUBVPz4+pUmUEAwc2ZuDAQXh4VKJXr97Uq/ck27Zto5AMFQThAYW2NB6UlZWFh4dHkXbaps1LHDkyAWj9hzWDcZOvxEWhoEtgIDVcXUmzWjmQksIdoxGDzQbkL0el+pJFi7wZPHjw/WU2m43Zs2fzxRdfYzIZsdsrY7W+id0eQP36Gxg37t+EhspRqSQuX4aMDAM5OXrmzh1ESEgVli1bg6enNzqdEb0+g9Wrf2Xt2s9QKILx87MQHj6V/v37F+k7C0JF8ZdvfhU1MAA6d26FQhFVyJrFGOxj0Vks/HDnDuHXrvHdjRvE5uRgtD0P3CnwCa32ALVq1cq3TKFQMGXKFDIyUtm1aydt2tTHxWU+CsV14uJOcPHiSU6ezOboUQPp6ZkYDFlcuHCA7Ow0Zs78Em/vIIKCfPH21gKuuLm9RGBgR3Jy+nHr1rfs3CmmohSEh/nLlsajOHLkCF26vENW1oWHbGEC/gMcBAKAt4BKhWyXgVYbSkrKjYdOi/A/MTExzJw5l/Xrf0Amk+jadTB167bBZDJy4cJeDh3ailbrwU8/7aV+fR+MRjes1mzS01M5ftxAVNQmfvklBje3zcTHwyNkpSBUCCUSGpIkUbfuk1y7NoO8d04ejVI5jX/9K5mVKxf97c8kJyczfvwE1q//AZvNjkymATpitY5Eo+nHL7/sQKHwxsVFRXa2Cb0+i6tXc9m37wf27ctk9uw1wFcEBgbSr18/0SlMEP6gRAamkMlkrFjxLZ6eM4DcR9zLVVxcFvPZZ1OK9KmAgABWrVpGRkY68+Z9jb9/ABpNApCOxeLPkiW7uXRJT3x8GleuZHHtmoGcnHROnfoVD48+DB8ODRo0YOnSpYSEhBAeHo5Op3vE7yAI5Y9ixowZM0pixzVq1MBgyODMmQWYzd0BVRE+fQ2NpiNLl35NWNgfb6b+PSqVipYtWzB27AgaNKjElStz0emSiY7ei1zugotLVXJzc0lKusMPP4STmlqP+fOn07y5jJCQEFQqFcOHD2fnzp2MGDGCW7duUbduXfz8/B6pntJk7ty5fP7556xbt45t27aRkpJCo0aNUCj+2K9GEAohlSCbzSZ169ZPcnfvIEGSBNLf+CdSql69m7Rw4eJir+fo0aNS69bPSWq1q6RUukoaTYCkUGglheI9qWFDq2Sz5W2XnJwsvfDCC1LlypWlTz/9VLp06ZI0depUKSAgQOrevbt08OBBSZIkyW63S7m5uZJer5dycnIkq9Va7DWXhP79+0uzZ8+Wjh49Ku3atUvq37+/1KVLF8lutzu7NKEMKNFx8+RyOT//vI5Zs/ri6dkChWImkPqQrc+iVHajUqU3+eGHCbzzztBir6dVq1YcObKHK1cu0b//AOx2MypVX2y2YcyereB/owguWLCAcePGsWfPHm7cuEHbtm3x9fXl5s2b9OjRg+joaCwWCwkJCSQlJXHv3j3u3btHYmIiWVlZxV53SahXrx6tWrWiU6dOrFmzhrS0NM6ePevssioESZLIysoqs32CSnywTZlMxujR73Lx4kHefDMFT89GuLo2xc1tPK6uA/D07IWbWwi+vr1p187C/v07aNOmTYnWVLNmTVavjiAh4ToTJtTiqacm07173rpFixbh4uLCqFGjGDBgAB06dODixYt07NgRV1dX3n77bYYMGUJycvL94QNcXFwwGAykpaWh0+kwGAp2bCvN5HI57du35/Dhw84upVyTJIl58+bRuHFjwsLCqF+/Pjt27HB2WUXmsEcDNWrUICJiHnPmTGPatGmo1TY0mho0btwYT8+hpKSkEBMTg0aj+eudFRNfX1+mT5/M9Om/L0tMTGThwoWEhYXRpk0bli1bxoQJExg9ejTVq1fHy8uL7OxsjEYj7u7u+Pj4YDKZsNvtpKWlkZaWhlwux83NzWHfozhYLBYxYHMJW7RoETt37uTIkSNotVquXbtGu3bt2Ldv35++AFraOPynRCaT4e/vT6NGjejcuTMtWrTA09PT0WU81Mcff8yNGzfo3LkzERERaLVatm3bxsWLF6lZsyZjx44lNjYWs9mM3W7HZrMhSRK2/3aN1+l0yGSyMtf0PHToEK1atXJ2GeXasmXLmDFjBlqtFoDatWuzdetW/P39nVxZ0YhOCIVwc3Pj3XffZdiwYcTHx1O7dm1WrVrF3bt3+eabbzh69CgdOnQgKysLq9WK3W4nOzsbu92OxWL56wOUAnfv3iUmJoacnBx27NiBVqsVM9mVsLi4uALnuHnz5k6q5tGJ0PgTcrmc2rVr3///qlWrEh4eTmZmJomJieTk5JCZmYlMJkMmk6HX61Gr1dhstlI90/3jjz/Oli1b2LJlCxqNhrCwMHbu3IlKVZTH4kJReXh4kJ2djbv774NT6fV6tFptmbo0FKHxCLRaLR4eHhgMBoxGI5IkYTQakclk1KlTp9QP8DN58mQmT57s7DIqnGeffZZffvmFN9544/6ygQMH0q9fP/71r385sbKiEaHxCBQKBYGBgcjlcoxGI9nZ2ajVatzd3fHz8/vL92RKi1OnTrFo0SJOnz6Nm5sb6enpzi6pXAkNDaVbt2689dZbAEyaNImuXbsSHx9Pw4YN2bZtGzqdjj59+ji50qIRofGIlEolQUFBWCwWrFYrcrkctVpdJpqZubm5zJgxg88///z3hZUqQerD+tAIj+K6zcb2HTvuh0a9evWIjIzkp59+4sSJE3To0IEBAwagVqudXGnRiND4B2QyGWq1ukz9od+7d48ePXpw8tQpZM2aITVrBl26gL8/2O3OLq98OHIEPvkE99xcnv7DiHDBwcGMGzfOSYUVDxEaFcj58+fp1r07d27fBh8fpLlzoV07Z5dVvsydC5MmgSTxREgIy5cvd3ZFxa70t6WFYrFt2zbatG2bFxh168KJEyIwipPFAkOGwPjxIEm88cYb7Nmzp1y84PhHIjQqgLlz5/JSz57kZGdDhw5w7Bg88ChZ+Id0OujcGb77DmQyZs+ezYoVK8rUZWtRiMuTcsxqtTJ8+HAiIiLyFrz1FixcCKI/RvGJjYVu3SAuDo2bG2u+/55evXo5u6oSJUKjnNLpdLz88stERkaCTAaff57XdBaKT2QkvPwy6HS4a905EHWAJ5980tlVlTgRGuXQtWvX6NatGzExMeDmBmvXwkuPPuyiUIiICBg+HKxWVEFufPLBJxUiMECERrkTFRVFr9690aWnQ7Vq8PPP0LSps8sqP+z2vBbbV18B4N0nBI2kJigoyMmFOY64EVqOLF++nI7PP58XGM2b5z0hEYFRfLKz81ps/w2MoElNqLmxI4oAV8xms5OLcxwRGuWAJElMmDCBwYMHY7VYoE8fiIqCypWdXVr5cesWtGkD27cjU8sJXtWeqp+1zOvg1ymAb5YuwGqtGPPliNAo4wwGA3369CE8PDxvwYQJsHFj3r0MoXgcPw4tW8KFCyj9Xakb2Q2/138fNMe7ZzC6lvDCy93KzNAI/4QIjTLs7t27PPPMM2zevDnvMeqKFTB7dt7TEqF4rFuX1wkuKQmlVk3o8Z5o2+S/fyGTyfANb0K0+iYDhw1yUqGOI0KjjDpz5gwtWrbk9OnT4OcHe/fCA69cC8Vgxgx49VUwmWjevDmVu9TGJaTwUeZkSjmV17Rl7/XDzJkb7uBCHUuERhm0efNm2j79NIkJCRAamtd8fvppZ5dVfhiNeWHx8ccAjBw5ktWrVyO7mkvql9EP/ZhMJafyhqeZM//fnDx50lHVOpwIjTImPDyc3n36kGswwHPPwdGj8IcJsoV/ICkJ2reHdeuQKxR8++23zJ8/n9DQUE5FHqfSVisJvaMw38ou9OOqQDf8F7fktSGvl9v7GyI0ygiLxcLgwYOZMGFC3pxSQ4fCL7+At7ezSys/LlzIu+F5/DieXl7s3LGDESNG3F/t7+/P8cgjjA57k7vt9pDydTSSpeBwAl6dq6OvYmPp8qWOrN5hRGiUAWlpaTz//PN5r1nLZPDll7B4MYjJqYvP9u0QFga3blGzZk2OHT1K586dC2ymUCiYMP4jLhw6Q51ILfc678dwPq3Adt7TGjLryzmOqNzhRGiUcjExMbRq1YqoqChwd8/r4Tl2rLPLKl/mzoUePSAnh7Zt23L8+HHq16//px+pWrUqe37exVfvzSLhxX1k7UvIt17bKpBcFwuXL18uycqdQoRGKRYZGUmr1q25du0aVK8Ohw/nvVEpFA+LJe8y74ExMPbu3UulSpX+9i769ejL/u17SXr9SIH7HG4dq3Dp0qXirtrpRGiUUhEREXTq3JkMnQ5atMjrEt64sbPLKj90urxhDiMiQCZj1qxZjzwGRpMmTfh00gwyJl3It1zeRMuew5HFVXGpIUKjlLHb7YwbN46hQ4dis1qhb9+8LuEV6IWoEhcXB61aQWQkGjc3fvrxRyZOnPiPdvnu0HcxHEnGbrbdX+ZS05Or8bH/tNpSR4RGKZKdnU3Pnj358ssv8xZMngzr14MD57ct9/btg6eegthYKlepwqGDB+ndu/c/3q1SqeTp59thvJzx+0KFjDs3b//jfZc2IjRKidu3b9O2bVu2bduW1yV81SqYOVN0CS9O330HnTqBTkezZs04dfJksY6B4YIaS2LO7wskcPfQFtv+SwsRGqXAyZMnadGyJefPn8+bfyQyEl5/3dlllR92O4wblzfwr9VK7969OXDgAFWqVCnWw0iSPV/IGy/raPlk2Zur9a+I0HCyjRs38ky7diTduwf16+d1CW/b1tlllR/Z2dCzZ17fFmDixIn8+OOPuJXAW8ApulRUQb9fSlp/ukffF8vW7Gl/hwgNJ5o5cyb9XnkFY24uPP98XpfwmjWdXVb58b8xMLZtQ6VWs3LlSmbNmlVik3PHXonFNTSvh27WgUSUNyx06tSpRI7lTKJLoROYzWbefvttVq9enbfgnXdg/nzRw7M4HT+eN8pWUhJ+lSqxZfNm2pZgCy42NhbJV4ncNe/PMP2jcyz4+IsSCyhnEj+lDpaamkqvXr04dOgQyOV5zeYxY5xdVvmybh0MGgQmE/Xr12f79u3ULOEW3LcRC3Dpn3ePJO37OALtPrzc5+USPaaziNBwoCtXrtCtWzfi4+NBq817nPrCC84uq3yZMeP+K+2dOnViw4YNeHl5leghU1JSWLFqJbVie2G6kYVuwnl2/HqwTEwG/ijK57cqhX799VdatW6dFxg1auRNEiwCo/j8YQyMESNGsHPnzhIPDICJH0/Gc2BN5G5K9O9f4POP59CgQYMSP66ziNBwgIULF/LCiy+iz8zM61h04gQ88YSzyyo//jAGxvz58/n2229RKBQlfuijR4+y8ecfqTS5EekzL9LGtwlD3xpS4sd1JhEa/0BKSgodO3YkJSWl0PU2m43Ro0czfPjwvC7h/fvD/v0QGOjgSsuxB8bA8PD0ZOeOHYwcOdIhh87JyWHC3KkELm1N7tk07D8mEzFvsUOO7UwiNP6B5cuXYzAYWLlyZYF1WVlZ9OjRg/nz5+ctmDYtb6YzV1cHV1mOPTAGRkhIyEPHwCgpoz8YQ3yVNDSN/Uh68yibVm3E3d3dYcd3FhEaj8hut7N06VKWLVvGqlWrkCTp/rqEhATCwsLYuXMnqNWwZk3etXY5fPzmNN98k28MjBMnTjj0PkJMTAzrf9pIpc+akDzkGB+NHE+zZs0cdnxnEk9PHtHu3bsJDQ0lNDSUJ554gv3799OhQwcA+vTpQ4pcDl5eefOQuLnBli1OrrgcUCohIQE2bUJ19y6o1bz6yitERESgVqvR6/V07dr1/uYBAQGMGDGCjh07Fnspkz6dgu/Y+mRsvUkrv8Z89P6HxX6M0kqExiNauHAhkiTx6aefYrFYWLJkCR06dMBoNHL6zBmUDRpAZib8w1euhQdUCYKEewAoNBq+njePYcOG3V9ts9mIjY3l6NGj2O124uLiGDBgABcvXsTf37/YykhNTWXXr79Sa15PrtffzJyDJ8vt49XCiNB4BHfu3OHMmTNMmTIFgMDAQMLDw0lJScHf35/169axY8cOrvz3/Qaj0ci5C+fQtCz4g2uJzuTx2g1wdeK9jvPRF7DVUGG7nUvdarUc8pjyrxw/eRzXFvlH0FJWcsF4wp1OLZ5lyZIlhU66rFQqqV27NgB169YlKCiI1NTUYg2Nrdu24tM7GMPxZFq2fop69eoV277LAhEajyAiIoJXXnmFoUOH3l92584dVq5cyfjx4+nVqxe9evW6v06v11O5ZlVCD79UYF8pvQ6xZMoSp14PfzrrU5a4/weZTEa7pOYs+Gye02qBvHFFgp+sTXAh5yu5+0GmTZv20FnaMzIyGDhwIDabjfj4eJo3b05oaGix1rf5159xHVAFU1QK/V58u1j3XRZUnDZVMUpNTeWNP8xmNnjwYO7du1fo9p6entQMC0WyFhzuXuajRqfTlUidf6WtQT4AAApHSURBVFeQfxDE5eIeFsiR08ecWgtAeno6ar/C30L1ULv/aQhoNBrefPNN3nrrLd599132799f7BMXnTlzBvdWAVjPZlK7Zu1i3XdZIFoaj2DBggUFlgUHB/PFF188/ENpFnIvpuPW9A+D1vooSE9PL+YKH85ms7F7924uX75MkyZNaNOmDUqlEpcANzSNfPntYpTDanmYtLQ0VH4FL9fsZhvxey6h1T58YBsXF5f7N6QBbty4wfbt22nZsmWx1Ga328nWZ1PFzxWPEF9sNhs5OTns37+fmJgY2rZtW2zHKq1EaDiIUqHEmJxbYLnNV+GwlobNZuONEW+yJ+YQyra+uKz4nsSXY3Hx1hD4fRgylZzMpAysVitKJ75xm56ejtyv4AC/MpnsL98aNZvNHD58GMjrK7N27VrmzSu+y607d+7cb59bO3rS5/W+KF1VeD1dBVtNF2YODGfOhzMZOrj89goVoeEAkiSRcCeBys0aFlgn81GRrCu8R2lJ2LxhE/VSX71/t9+HFvnWq91dsFgsTg2NtLQ08FMVWC5TydGG+HLlypVC5yVRqVQ8//zz9zvUeXl5MX369GLt8PXgDWufvjXx6Zv/7dmszlVYPWeNCA3h0UmSxNSZ03Hp4I+yUsEmt9LHheSbjgkNu91OtaYhD308KFntuHm6o3HyQMbp6enY/Qp/b8RtaDBjpr7Pj8vW4+mZfwZ3rVbLunXrSrS2gIAAsEkPXa8KckNyySrRGpxNhEYJ+2jqBFbsX0fVXc8Vul7h40JSumNCQ6VSociScdlvTeG9U2XwZPPiG2j3USWlJRfa0gCo9G4Drl4/Ratnwzi05wC+3r4Org4aNGrIhUprgELOoV2ifccOBZeXIyI0StD8hd+ydPtqahzojMK98F8Cpa8L6bqCc4GWBLvdzvZ1W/50QiCbzfbQdY5yLz0JZd2H91vx/7wZie8epWuvFzn06wFUqsLPbUnZvnYrRqPxoetdXFwcWI3jidAoIYcPH2bqnBk8dqIrCs+H/5KarutRqjTY7fYS71Uol8tLfASr4iBTyLEk5Dx8vVxGlcVh3BlwiPcmvM+CufMdWB1FmraxPBL9NEqATqdj3OcTCFrTBlVg4f0N7CYbyZPOYJlxjdkffloux5J8VB8OH4fHmmwSXzuENe3hf6MHLH6KnRf3cvz4cQdWJ4jQKAHD3x9JYmMT2raF91rMOZXC7ad+4ZnUBlw8fp6mTZuK0HhAcHAw5w6fZnBoH2633oX+1zuFbqdwV6EcF8yrb71WKi6rKgoRGsUsKSmJ7b/swG9iwZG5rKlG0t8/i23YFbYt+pHvl6zE29vbCVWWfiqVik+nfsLpX49RbYGZ5L6HyY0u2AnOq3N1cqvL2PjjRidUWTGJ0Chma9f/gM8rNZFr8t8uMlxI42br/zCkam8uHbtAq1atnFRh2RIcHEzk1t183ncq97ruJ23R1QLbuA+vxcLVS5xQXcUkQqOYbd//HzS9quZbZozJ4Oazu1j55XdMHDfB4Xf7y4P+/V7hwrFz8M0dUr6MzrfOq0t1zpw47aTKKh4RGsUsPUeH5vHf+w5IdomkN47wzb+/pkf3Hk6srOyrWrUqR/YeQhd+idwrv3e9l6nkVO1Qh99++82J1VUcDg8NNzc3atasiZubG3K5HLlcjlqtxsvLi7p16+Lr6/jOOsXFYDBwI/Y3lA+8bKX/5TZVFQEMHjTYiZWVH5UrV2bGpOlkzrmSb7nJ2543gbZQ4hzeT8PV1ZWBAwfmWxYcHOzoMkrErVu3UHnm79gjRefwwfD3xdORYjRk8NssO7A23zKzuyRaGg4iLk+KUU5ODhL530uwntZRvXp1J1VUPnl4eJBw/Ld845PYsZOT8/AOYULxEaFRjEJCQpBM+QfasefanDqUX3mlVKuQzL+fa5WeQt98FYqfCI1i5Ovri5RjxZr+ey9GhbeazMxMJ1ZVPpmNJmSa39+ENRxLqTBTCDibCI1iNmjQIHTfxWE35/VQtNdxJfpy9F98SiiKpKQkVD6a+/eJ9Hvu0KjhE+Xm3lhpJ0KjmI0dNob0f1/CFJPXunB5yo+te3c4uaryZc/ePbi2yntpTLLZSf/oHO/2rXgD/DqLCI1iVq1aNWZMnk76xLzHf9r2lTlz8jQZGRlOrqz8WLp+BS49KwOQ+n+XqesTQt+X+zq5qopDhEYJGD1iFG43JTK23kCuVuD9ak1mzw13dlnlwoULFzh78RxeXatjuWcgbWY0EQtFF3JHkkkPTkIqFJvTp0/zXK9OVDvYCblCzm9NtxN/+VqxTtpTET3X43muvWjC76263O0Sydiuw5gw7iNnl1WhiJZGCWnWrBkzJ39C8sCjKCu74TWwFpM+meLsssq0vZF7uZQaR6UhoaROO0+vxl0r1ByqpYVoaZQgSZLo0vsFrjZMw3fi49xu9h92rdkuHg0+grS0NB5v3QTfLa2xJOSQNewcMWevFBhcWCh5IjRKWFZWFk881RjlnDp5I1UPjyX62HmnThFQFvUd1J9TTybg0acGt1r/wr6tu2natKmzy6qQxOVJCfPw8GDHxm2kjTiNMkBDVm2Jz8JnObusMmXnf3ay5/g+fN6pQ9KAw3w6cYYIDCcSLQ0HWfzdEubs/Rb3zxryW/Pt3Iq7gZ+fn7PLKvUkSaJ2o7rIP6+N7aaBOr+6s2vTTmeXVaGJloaDDHt7KI/p/ck9l4ZPr2Ailn3n7JLKhMjISPTqXDQNfUmZeo6V/7fM2SVVeCI0HGji6A8xfncTzxF1WbFxtbPLKRMWrFiE+6ja6OZdZcQ7wwkKKnywZsFxxOWJA5nNZvwfC6T23b5cD9lE7MnLedP8CQ/lU8WP4NiXuPPUL5z79SRVq1b96w8JJUq0NBxIrVZTLbgGudHpeLWvysmTJ51dUqkWGxuLaw1P5K4KjMk5IjBKCREaDmC3/z7uQ9XqVbEkGrA3duPCpYtOrKr0u3r1Ki4NvLCmGvGvEZhv3YPnVHAsERolxGw2M/rD9/AM8EZbyZOnurfltaEDOX74GJqGPigDNFyNj3F2maVafHw8tspKlP6upCalMGT0MF4a0hfPIB/cfT0I69hWjFXiBCI0SkhcXBw7Y/dR63ovGqS/hmHBYxzrco/qkc+jrqYFIDnVMbPFl1VJKUnYlBIyhZwaezqxt/U1YodYqZPYlwa617jbzMT3a9c4u8wKR3RLLCE3b95E8lWg8Mib/NmlhhaXGtp82/zZ7O0CVA6qjDI970fUNdQb19A/zEZXW0P8DTGYsKOJ0Cghnp6eGK5nYJx1ttD1put66oa0cHBVZUv1atUx/ZpO4kPOoeFcKllBDRxclSBCo4S4uLgwoHUfTKnmQtfbPey0adHawVWVLY8//jiv1uuGPfUhNz2rQfun2zm2KEH00xAEoWjEjVBBEIpEhIYgCEUiQkMQhCIRoSEIQpGI0BAEoUhEaAiCUCQiNARBKBIRGoIgFIkIDUEQikSEhiAIRSJCQxCEIhGhIQhCkfw/zSJyTwr+cREAAAAASUVORK5CYII=)
A gun is firing 20 balls per seconds of mass 20 gm each on the smooth horizontal table surface ABCD. If the collision is perfectly elastic and balls are striking at the centre of table with a speed 5 m/sec at an angle of
with the vertical just before collision, then force exerted by one of the leg on ground is (assume total weight of the table is 0.2 kg and g = 10
)
![](data:image/png;base64,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)
physics-General
physics-
Three balls A, B and C
are placed on a smooth horizontal surface. Ball B collides with ball C with an initial velocity n as shown in the figure. Total number of collisions between the balls will be : (All collisions are elastic)
![](data:image/png;base64,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)
Three balls A, B and C
are placed on a smooth horizontal surface. Ball B collides with ball C with an initial velocity n as shown in the figure. Total number of collisions between the balls will be : (All collisions are elastic)
![](data:image/png;base64,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)
physics-General