Physics-
General
Easy
Question
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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)
- 12 mg
- 14 mg
- 8 mg
- 20 mg
The correct answer is: 14 mg
Related Questions to study
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,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)
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
physics-
In given figure, the small block of mass 2m is released from rest when the string is in horizontal position, Displacement of the ring when string makes an angle
with the vertical will be:
![](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, Displacement of the ring when string makes an angle
with the vertical will be:
![](data:image/png;base64,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)
physics-General
physics-
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 value of coefficient of restitution is
![](data:image/png;base64,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)
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 value of coefficient of restitution is
![](data:image/png;base64,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)
physics-General
physics-
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. If the kinetic energy lost is fully converted to heat then heat produced is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAABrCAYAAADKMDYpAAAVkklEQVR4nO3deVxN6R8H8E+rlhsphhZtKlptFaM9ZJetSfYkYsww9n3fZZkQknVESglTWmQtFWWGMIjfTKVRt5K61E11n98f7tzRtLjd7qJ63q9XrxfnPuc537zux9me8xwpQggBRVGQlnQBFPW1oGGgKC4aBoriomGgKC4aBoriomGgKC4aBoriomGgKC4aBoriomGgKC4aBoriomGgKC4aBoriomGgKC5ZSRdAUefPnYWioiIYDAaUGQwoKzPAYDCgoKCATp07Q0pKSix1SNHnGShJM9TVRlVVVa3lI0a54cChI2Krg4aBkrjsrCwAAJOZj62bNuBBejoAIP7GLRgZdxNbHfScgeKprq6u8cPhcMSyXU0tLcTHxWLaJE9kZ2VBVlYWzi4DxBoEgIaB+ox1T0t01dHi/fTt3QMhZ4NFus3UlGQMcx2ILRvXw8NzIk4Fh4DD4WDmLF+Rbrcu9ASaqmHZylWwsekHAHj48HcsX7IIaurqcB08RKjbYebnY+vmjYiMCIe1TV9ExyWgu4kJli1eCCNjY/S3sxPq9vhBw0DVYGhojD7W1gCAPtbWiIu5imdPnwotDFVVVTh14jj27NoBRUVF7PU/gNFjx0FKSgrviotxMfwCNm3dLrYrSJ+jYaDqVFVVhfjYGPz9dy6GDBsmlD5TU5KxZuUKZL54jukzvPHT4qVo27Yt73PV9u0RHZ8Abe0uQtleY9EwUDX8+P0cyMnLAYSgtLQUroOHQEdHt0l9fn5IZGVtg+i4BJiYmtbZ1tDQqEnbahJCUVy9zE1JXEwM7++vXr4k/ax6keVLFgnUX2VlJQkKPEJMjQxIH0szEh4WSjgcjrDKFTq6Z6DqZdC1K2bO8sXF8AuNXvdLh0RfIxoGql6EELx6mQkLS0u+1/nvIVFU7DWYmpmJsErhoXegKZ7eFmYw6NoVnTU0UFRUhPT796Davj0uXomClpZ2g+t+fpVIQUERq9auw5hx4yVyVUhQNAwUT/LdJJSVlUFeXp63zLJHT7Rr167B9VJTkrF21Qq8eP4c07y88dPiJV9c52tED5NaOUII4uNicTcxESnJSch88QLduneHrb0DDA0N0d+2/ptfTCYTWzdtQGREOPpYWTerQ6K60D1DK1ZRUYE5s2bi+rV4DHIdjH79bXmfPXmcgciIcIwaPQbbdu6CoqIS77N/Don2+u1EmzYKWLlmLcaOd29Wh0R1ktyFLEqS2Gw28Zo6mViYGJOkxDt1tklPSyMO/fuSCe7jCIvFIoQQkpqSTFxdHImeVmfibG9LYmOuirNskaJ7hlYq8FAAgo4ewa8x8fjmm2/qbfd3bi5cXRxhZdMXqqqqiIwIR28rK2zash2/nDqBmzeuIzHlPmRlW8ARt6TTSIlfeXk56WNpRo4dDeSr/bngM0RXsxPpaWZCws6HkOrqakIIIW/+/puYGOqTmKvRoixXbOgQ7laogJmPwsJCOLsM4Ku9vaMjZGVlse/AQYz/zgPS0p++Np01NDBv/gJsWrcWJSUloixZLFp9GKqrqxF15TJmzZiOXuam6Glugp7mJrDp3QNLFi5A8t0kkBZ2JJmUmAhDI2PoGxjw1V5LSxtq6uoo+/Ch1mfTvLzBes/CXr9dwi5T7FrAgZ7gAg8fQlDgYTDz8+E6eAg2b9sOGe6xb2FBAcLOh8DTfRwMDY2wd/8BWFj2kHDFwlFdXS20Kz/KysqY5TsH/nv3YMHCRVBt314o/UqEpI/TJOXXy5eIvrYG8Zo6mWQ8elhnGw6HQ64nXCPDXAcSCxNj8jgjQ8xVisbzZ38QXc1OJO/NG77aF799S4z1dcjNG9fr/JzFYhFL024kKPCIMMsUu1YZhtiYq8SgiybZumkjX6Mo2Ww2mT55IrHqYU4+fHgvhgpFq7ysjPS2MCMnjwfx1T7k7KcT6IqKinrb+O/bSya4jxNWiRLR6sLA4XDIAEd7MmH82EYNJ/7w4T3pbWFGNm9cL8LqxOfQwf3EpncPwmQyG2z3KjOTmHczJLNmTG+wXU5ODunWVY/kvn4tzDLFqtWdQN+/l4qXmS/ww/wFjTpuVlJSxuy53+PksSAUv30rwgrFY/LU6VBRaYtBzg5ITUmus83vvz2Az4zpMDUzx669PzfYX7t27WBsbIzgX06JolyxaHVhuHL5EqysbfBtA2Nu6jN56lSoqLRFXOxVEVQmXgwGA+GRl6GhoQGPcWPgO3MGTh4Pwt2kRJw+eQJLFi7A2FEj0E61HX4+EPDFZxFUVFTg4OiEmzeuN9urbw3egX6Qno7E27fw/Pkz/PXn/yAnJw9rGxt0/KYTRo5yg4ampjhrFYphrgPg4TkR07y8BVr/px/nQU5ODjt37xVyZZLB4XAQezUax4OO4nFGBsrLy9C2bVsYd+uOkW5umDx1OmRkZPjq64+nTzF0kAuCQ8Jga28v4sqFr85LqwUFBTgRdBQBB/zRrXt3mFtYYpy7B9jsciQl3sGLiHAcPRyARUuXw91jAt//WJJWVvYBL54/h7S04PXKyMg02//56iItLY2hw0dg6PARYLFYKCl5BzU1NSgpKTe6LxNTU5iYmuLmjYSWEYb8vDxMcB8LGWkZnAo+BwdHpxrH1nPn/Qh2eTnOnT2D9WtWIyX5Lnbv828WgVBUVELHBsbhtHYqKipQUVFpUh99+/XHq1evhFSReNUIA5PJhOd34yAvL49zYeFQU1OvcyUFRUV4efugW3cTeE+bCmXlFdiyfadYCm6K6upqqKmpoaiwUOA+ioqKoNkMDw/FRUlZCWx2uaTLEAjvBJoQAt+ZXlBX74DL0bH1BuFz/W3tEJtwAxfCQnE1OkqkhQqDlJQUrG36IiI8rM5Zn7+EyWQi6c5t2Ds6iaC6lkFOVhaPHz1CeXnzCwQvDJkvnuNBejoWLFyMNm3a8N2Bjq4uJk6ajG2bNwo8US0hBFcuReL9+/cCrc8vGRkZTJo6DdlZWbhyKbLR6x8JOABFJSU4OTmLoLqWYfTY8SgtLcXN6wmSLqXReGH45dRJGBoaCTTH5fQZM5GdlYXbt24KVEROdjY2rF2NgU72iI+NFagPfhkZGcPapi8O+v8MNpvN93q5ua9x5vQpLFqyDAqKiiKssHnTNzCAuro6qsU0g7cw8cKQlHgH7h4TBBrApaunhz5W1ki6c1ugInR0dXHt5h3Y2tnDZ8Y0+Pp4Iz8vT6C++LFp63YUFhVitrcXX4HIz8vDFE8PGBl3w6QpU0VWV0shKycH6Xq+R48zHiHt/r1aRxEFBQW4GH4B74qLecuKCgsRGnKu3puCwiYLAJWVlShgMvFNp04Cd6SupobfHjxA4KEAgfvo1q07+tvZISY6CjHRUdi6Yxc8J00W+rO13U1MEBwShimeHnCxt8W8+Qsw/juPGrNCAEBJSQlOBB3FsaNHoKmlhVPBZ5vFVbOvESEESxYuwLt3xVBX74AFP8xDVEwc2qmqIurKZVwIPQ9DIyPs3b0Lp86cg76BAfbs2gFbB0dcuhgBVVVVdOtuItIaZQGg7MMHfKhjrHpjcAjBX3/+iahfrzSpHxarlPfn6F+vYOiw4WivptakPutiZm6Om0nJ2L5lE1YuW4KA/f4YNnIkZGU+XWArKGAiJjoKHysrMf+nhfCZPQdycnJCr6O1uBR5Ee9ZLASdOA0A8N+7B+npabC1s8eKpYtx5WocdPX0oKCoiI3r1uDEL8EoZ7Ph6OSM8rIyZGVliScM7VRVoaWtjY8fPwrcEQEw0s0N6zZuFriPhPg4rFy+FKrt22PNug0in3Ghbdu22LpjF+Z8Pw+XL0Ui7d6/u295eXksW7kaw0aM4OvKGtWwSxHh8Jw8BS9fZiInOxtj3d2hrd0F6WlpaNu2HXT19AAAtnb2CD79KTCzfOdi+ZJFsLa2wTj370ReI+8+g6GRMaJ/vQIPz4mN7oTFYiHx9i2sWb9RoCKK377F+rWrceliBMaOd8fqdevF+gXsoqOL73+YL7bttVYnjweBocyAtIwMnj55jMhfo1FaWoKuhoa8NoZG/87C3d3EBPsDDoutPl4YJk+ZCp8Z0/H6dU6j58e/HHkRsrKycBszVqAiSktLwWQyceZcKOwcHATqg/o6VFVVgVVaCjk5+VqfaWvrYOfuPQCAfbv9cPbMGZiZm9d4Oq6iokJstf4X72qSg5Mz2rdXw5GAg43q4OPHjwjY748JEycJfCtfV08P50Iv0CC0AE+fPEZZWRkse9R+RFbts3M/NXV1VFVWQkpKCqWl/54nZjx6BA1NDbHU+l+8MMjJycFv38+4EBoKvx3b+BqMVvz2LbymTgJDhYEVq9eKtFCqeUhNSQHw6cv+OTNzc7x6mQlCCCorK5F2LxXmFhbo3ccK91KSkZn5AgCQePsWhg4fKfa6gf+MTXJ2GYD9AYfg6+ONktJSrFi1ut7Ri69f52C2txdKS0sRGh7ZMiaRauU+P0RpzCiEz5WUvEPHjh1rfR9mzvLF7Jkz4DZ8KCoq2HB0dsGAQa6QkpLCspWrMdF9HLro6EBBURFLV6xq0u8hqFrPMxBCEHz6FE4cP4aSd8WYMs0LFpaWMDO3AJvNRlLiHTx6+DvCw0LR79v+2O63+4vTlVNft7T797DHbyfuJibyljk6OcPDcyKGDh/RqCt68+fNRVVVFQ4eDqz1GSEEWX/9BSVl5Vqz+L19W4SioiIYGRkL/os0Ub0P91RWVsJvx3bcvJGA1zk5vPsQmppa6NS5E6Z7+8Bt9BixFksJV35eHhb/NB+/PUiHu8cEuA4ZCkVFRbBYLCTduYOI8DBY9uiB5avW8PWuNQ6HA5telpg3fwGmz5gpht9AuPiaa5XFYqGosBBy8nLQ1NRq/rMtU2Cz2RjmOgDy8vI4ExKKDh061mpTWFiApYsWIuvPPxFxJeqL71zIePQQI4cORvyNWzAy7iaq0kWGr2egVVRUoKevDy0tbRqEFoDD4eDk8WPgcDgIPh9WZxAAoEOHjti5ew9KWaVYv+bLx/HX4uMweuy4ZhkEoBVOCEB9uhx+IugofGbPgbp6hwbbdujQEctXfroh2tAzIOzycpw4FoRRzfjQmYahFcrO+gv5+Xl8Tzzs4OQMaWlp3L+XWm+b9LQ0lJaUwMraRlhlih0NQyuUfDcJ+gYGfM9u0rFjR6ipq9cYXv05Qgj27fGDg6PTV/9624bwFQZmfj6se1ogKPCIqOuRCEII+lia835cHGyxdNFCvH6dI+nSREJGRhYfKz4K/GTif12Li8P9e6mYv3CxUPqTFL7CEBYaAk0tbZw+eVxo/4Bfm6KiQszw8cGmrduweOlyyMrKYJjrQLx9WyTp0oTOzt4BubmvkZOdzVf73NzXKGAy0Vmj7mESoSFnYWfvgD5WVsIsU/y+NP9kdXU1setnTR6kpxHbvtYk6c5toc9xKWkcDofoanYiD9LTaiwb4GBHEq7FS7Ay0aiuriYDHO1J4OFDfLU/djSQGOpqk8rKylqfvXv3jpgaGZDUlGRhlyl2X9wz3E1MRHVVNXr26g1nFxecDT4jjoxK3JPHGSgoLIC5uYWkSxE6aWlpzJu/AIGHDn7xkcqnT57Ab+d2VFZWYoqnBzJfPK/x+bGjR2DZoyds+vYTZcni8aW0zJ3tQzZvWEcIIeRBehox1NUmRUWFIk+pOP2zZ+hpZkJsevcgNr17EGN9HbJ6xbJGzdTdnFRVVZEf5swmFibG5NkfT+tsk5n5ggxydiReUyeTm9cTiIu9LW8q//fv35Mnjx8TYwNd8ujh72KuXjQaHF1XVFSI2KvRmOU7F5cjL4IAUFBQQHhYGHxm+4opruLj5T0Tuvr6AID8vDfYuW0rtLS14Tt3noQrEz4ZGRn47fPHhrWrMXLoYOjo6sFnti9vOMbpk8eR+eIFps/wxrKVq9GmTRtctbXDsaNH8POePbgUGQHVdqpwGz2mxbzRqMHhGIGHAnDo4AEMH/nvkNqXmZlgMvORcCuxxdyNJoRAX1sDF69EoVfvPgA+jc3avXMHnjzOwC/nzku4QtHKycmG3/ZtSL6bBEhJQUpKCq6Dh+C7CZ51ftH/zs3FxvVrERMdhX7f9sfWHbtg0LWrBCoXsvp2GRwOhzjb9yfrVq+qsTzvzRti0EWzRZww/aOuE2hCCFmycAGZM2umhKoSr/Kyskavc/PGdeLQvy8x1NUmu7ZvJWVlH0RQmfjUu2dITUmGx7gxuBB5udZdxfnz5kJaWhp7/Q+IJbCiRrh7hhGj3HhDi58+eYJXLzNxPjyyZfyvJyJsNhtHDx/CAf996NChI9Zv2oJBgwdLuiyB1BuGxxkZeP7sD4wZN5733t9/5GRn4ffffsNIt9FiKVLUCCEIDwuttdzB0alJc0k1Z4QQcDgcvueJysnOwoZ1a3AtLg4uAwdh/cbN0NHVFXGVQibBvRL1FQs44E90NTuR58/+aNR61+Jiia2NFTHW1yH7dvuR8vJyEVUofHw9z0C1LoQQONl9CwZDBX379cPaDZsatT67vBwHD/jj8MED0NDUxIbNW/keFChJdKAeVUtK8l3Iycphw+YtCL8Q1qgJmoFP7+9YtGQZ4m/chr6+AbymTMJsby/k5r4WUcXCQcNA1RISfAbDRo6ElbUNtLW7IOZqtED96Onr4+SZszh09BgePXoIFwc7HNz/c5NmbhQlGgaqhnfFxbgaHYVh3OlaRowahZAmDMGRkpLC0GHDkXDrDmZ4+2Cv3y4MGeiMxNt1z9jO4XAk9s48GgaqhojwC5CWlsGd27cQFHgEBUwmUpLv4n9NfE+bkpIylq1chZiEG+jUWQOTPb/D976zkPfmDa/Nu+JijBgyCGn37zX11xAIDQPFQwjBueAz6G9nh/KyMpR9+ABV1fYw6NoVIeeChbINQ0MjnD0fhv0Bh3H/XipcHGwRePgQKisr0U5VFQqKijgmqedmJHoti/qqpKelEYMumiTvzZsayyMuhJFe5qakoqJCqNtjsVhk84Z1RF9bgwx0ciDJd5PIzRvXiZ5WZ5Kd9ZdQt8UPumegeELOnsGIUW7o1LlzjeXDR46CjIw04mNjhLo9BoOBVWvX42p8AlRVVTFh/FhEXAiDpqYWTh4/JtRt8YPeZ6B47t9LhY6Obq0wAMCzP/6AjKyMyGa8I4TgYvgFbNm4AUVFn15NnPEss8nvpW4MGgZK4tyGD+VNQ1NaWsJ7HHXxshWY96P43ptBZwumJE5NTQ1tFBTAYDCgrMwAg6EMRSVlqKurgxAitkcF6J6BorjoCTRFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcdEwUBQXDQNFcf0fRZoQNMmO+AYAAAAASUVORK5CYII=)
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. If the kinetic energy lost is fully converted to heat then heat produced is
![](data:image/png;base64,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)
physics-General
physics-
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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)
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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)
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 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,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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 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,iVBORw0KGgoAAAANSUhEUgAAAMUAAABVCAYAAAD5XiCzAAARkElEQVR4nO3dy3NbZ8HH8e/RObrfbFmWb7rYkWzZbmzcmIQQDyVTumiYUggDC9gxw4YtK/bAv8CCYQEbhhmY6Y5Cm1KYoZiWkEtzsS1fa8m2JCPJsiTrfvQuMjoTK3FoG0vidZ7PTBaxrPMcXX7Pea7HUqPRaCAIgkbX7RMQhP81IhSC0EKEQhBaiFAIQgsRCkFoIUIhCC1EKAShhdLtE/j/RlVVarUaOp1O+yecLeIT/YzK5TLZbJajoyOq1Wq3T0doAxGKzygajfLHP/6RO3fukEwmu306QhuI5tNn9J///Ifbt28jSRJ9fX00Gg3K5TKNRgNZltHr9UiS1O3TFJ6DCMVzqtfr7O/vo6oqFouFnp4e9Hp9t09LeA4iFM9hZ2eHWCzGrVu3CIVCvPrqq+IqcQaIUHwOqqqSSCRIJpNks1mKxSLj4+MYjUYRijNAhOJzqFar3Lx5k2w2i9Fo5Cc/+Qlf+MIXsFgs3T414RSceigKhQKHh4eUSiVUVT3twz+T1WrF4XBgMpnaPn9Qq9UoFouUy2VqtVpby3qa5eVl/vGPf5DP56nX6x0rV1EUZmZmuHr1asfK7LRTD0U0GuXevXvaiEwnmhONRoNarcbIyAjj4+MMDw9jNBrbVp5Op2NoaAi73U6lUmF9fZ3+/n4mJyfbVmar7e1t3nnnHZxOJwaDoSNlqqpKOp1Gr9eLUHwWH3/8Mb/+9a+14UlZlk+7iCeoqko+n2d2dhYAl8vV1lDo9XouXLiA1WollUrxt7/9DVVVCYfDHetTpNNp1tfX+c53voPP5+tImdVqlRs3bnB0dNSR8rrl1ENRq9VQFIUrV67g8XgwmUynXcQTyuUyd+/exel0tr0pIcsyJpMJvV6Pz+djYmKClZUVEokE//73v5mamsJqtbb1HB4/F7fbzfDwcEfKq1ar2Gw2FOVsd0VP/dWpqoosy3i9XgKBQEc6n0dHR8RiMQwGA41Gg3ZuO3e73Vy4cAG/34/X68XpdHL58mUajUbH10FJkoTFYsFut3ekvEqlgsFgOPPrvc525NsgGAwSDAaP/ey73/1ul85GaIezHXlB+Bxe6CvF5uYme3t7VCoVJicnGRwcBKBYLBKNRrlz5w4LCwuMjIxoz9na2uLu3buEw2GGhoZwOp0ApFIpdnZ22N3dJRAIMDU1pT0nk8nwwQcf4Pf7GR8fx2QyIUkS2WyWSCRCqVSip6eHl1566cw3TT6N5tKZ5eXlJx4zmUz09PTg8/na1nd7oUPx4Ycf8t5775HNZvnRj36khSKdTvPXv/6Vn/70p/zyl79keHgYSZJoNBp89NFH/PznP+eHP/whr732mhaKra0t3n77bd577z2+/e1vMzk5qT0nFovxs5/9jDfffJMf/OAHeDweZFkmHo/z29/+llQqxfT0NOFwuGPDq//LKpUKS0tL/OIXv8BgMBwbwezv7yccDvP1r39dhKIdUqkUW1tbFAqFY8OMsViMnZ0djEYjxWKRQqGAzWbTJuvg0TzB3t6edkVIJpMsLS0Bj0bgMpkMTqeTUqnE4eEhBoOB/f191tbW6O3tRZZlSqUS0WiUVCqFx+Np6wDB/yeqqpLJZHj48CHf+973jl11LRYL/f39OByOtpX/Qoai0WhQr9cpFAoUCgVUVaVUKlEqlTCZTNoXdWxsjMPDQ5LJJBaLhUQiQblcxuv1Eo/HicfjwKMPMZvNkkgkGBgYQKfTsb29TTgcJp1Ok0wmGRoa4ujoiNXVVV5++WXq9TqlUolcLkexWKRSqVAqlVAUpSNzO92Uy+VYXV3FYDDQ29vL4ODgsdfcaDSoVqvkcjkCgQBf/OIXtccURcFkMmE2m9t2fl0LRXPotNnEUFUVnU6HJElIkqTNNzT//6xJseaxKpUKhUKBbDZ74u+azWZkWSafz1OtVjEYDFgsFiqViraWKRaLkc/nmZ+fJ5vNsr29TSAQYHNzk3K5zOzsLPfv3yeRSKCqKuVymaOjI+r1OlNTUyiKwvLyMoFAgEQiwc7ODpOTk+zt7bG+vk61WkWSJIrFIjqdDrPZjKIoZLNZDAYDiqJQLBafObzcLE9V1WeuHFBVVStPkiSq1So6nU77EjaPIctyxwKZTqd55513MBqNnDt3jsuXL2Oz2TAajcfmQHQ6HTabjd7eXu1ner1e65O1S9dCUavVODw8xGg0Uq/XSaVSWK1WbDYbZrOZ/f19yuUyFosFh8PxzBnqRqPB4eEhm5ubfPTRR9y4cePE3//Wt77Fyy+/TCQSwWQycf78eWw2G4VCgc3NTdxuN6lUCkmS+MpXvsLt27fZ3t5GVVU2NzcplUpcuHCBzc1NKpUK+Xye3d1darUa4XCYmZkZ4vE4KysrXL16lXg8zt7eHvPz8+RyOZLJJPV6nd3dXfb395mYmKBer9PX18fS0hKKopDJZPjd735HoVA4cV1VJBJhf3+fg4MDSqXSiTVnPp/nX//6F1arFYPBwP379xkYGGBoaAhZltnY2CCXyzE8PMzU1BQDAwOf/cP8jPR6PS6Xiw8++IA//elPvPXWW1y9epXLly8zMTEBPJooPDg44A9/+AO3b9/WnjszM8Prr7+uVSTt0LVQ5HI57cU2Gg3y+Tzlchmj0cjAwAAHBwfkcjnK5TIXL17E7/c/s2OlKAp2ux29Xk8gEHhiJj2Xy/HgwQNisRhut5v79+9jMpmYnZ3FbreTSCRYWVlhbGyMRqOB2+1mZmaGv//978TjcVRVJRqNotfrmZqawu/3o9Pp2NraYm1tjVqtxvnz55mYmCCZTLK9vU25XCaVSrG/v8/o6CgbGxusr6+TSqXY2NggkUgwOTmJLMuoqsrS0hIOh4PDw0PW1tYIhULHasnHZTIZNjY2UBTlmSNWhUKBO3fu4HQ6GRgYQFVVIpEIq6ureDwerZmyubmpVUDPaprUajXW1tZ46623nvXxPlOzAtvf32dnZ4doNEoul2NnZ4fLly/j8/lQVRVJkjCbzdhsNu25zavEmbxSZLNZ/vnPf1IqlTAajVgsFlZWViiXy9rehHQ6zcrKivZhnRQKnU6HxWIhHA4zOTnJl7/8ZW1UqCkajfKb3/yGYrHI8vIyH3/8MbOzs0xPT2O329nc3CQejxMOhzGbzQwODuL1eqlUKqTTaYrFIslkkoGBAUZHR5mcnCSfz/PgwQMikQi9vb3Mzs7i9/tRFIV0Ok2hUCCTyXB4eIjH4yEQCHBwcEA0GuXhw4ccHBzw6quvYjKZiMVi3LhxA4fDobW133jjDW09V6vf//73RCIR7Hb7M0esyuUy6+vruN1uent7mZ6e5s9//jPLy8vMz89z/vx5rFYr77//PuFwmLGxsRND0Vx4ubGxofWnPo9mc1mSJJxOJ7u7uywuLvLJJ59wcHDAtWvXaDQaWCwWLl26xMLCgvZcp9OJ0Whs69B11zvaXq+XUCjExMQE7777Lru7u4yNjTE9Pa2N+tTrdTKZzLH5glaSJGmLEA0GwxPNp+Y8QDqd5t69eywtLXHx4kVtGLT55bl37x4OhwO/348kSbjdbrLZLLdu3UKn02mrUoPBoBau1dVVrly5Qjgc1sbRm82hXC5Hf38/iqIwPDxMMpkkEonw8OFDjEYjwWAQm81GPp9nbW0Nq9XK2NgYc3NzuN3uE5uBzb3gn7bWDAQCXLp0CafTyYMHDygWi1y5coVAIEA8Hsfr9WIwGKjVaif2USRJQq/XMz8/zze/+c3/WuZJqtUqmUyGxcVFFhcXyWazBINBXnnlFa5fv87Q0BDJZBK9Xs/g4CBjY2Pac5t9nzN5pWjq6elhZGSEkZER3G43xWKRvr4+hoaGyOfzuFwurYP4aZx0Pyar1crU1BR/+ctfiEQilMtlzGYzTqcTnU6H1WqlXC5z69YtLl68SCAQAB6F9ujoiMXFRaxWq9YWbzaHlpaWyGazyLKMy+VCURT6+/sZHh7m/v37lMtlRkdHMRgMDA8Pk0gkeP/990kmk4yOjuJwOLDb7VitVhqNBltbWzgcDq5du0Zvb++JNeJnbULYbDbcbrc2cmOxWHC73TidTnK5HGazGZ1O91/3wDQXIZ4/f/5Tl90qHo9z9+5drS8TCoWYnp5mZmaGqakpbR2ZTqfTWhGd1PVQmEwmLBYLkiShKApGoxGr1arVBrIsn0qt0BzpePvtt4nFYrhcLqxWqzba0t/fj9ls5u7du3z1q19lZGQESZIYHR1le3ubxcVFFhYW8Hq92n4KvV7PJ598gtPpxGQyabX6wMAAfr+fd999F5/Px/j4OAaDAY/Hg8fjYXV1lUajoYWoufK2r6+PeDxOJpMhHA6f6uRUs4Z93OdtgiiK8lxDopVKhTt37qCqKrOzs3zjG99gZGREW9hYKBQwGo24XK6uTGZ2PRRAR/YgyLKMzWbT2rOhUIienh7tca/Xy+DgIDdv3sRgMGiPjY6Oak2k69ev4/P5tGZEszZrXuWaPB4PY2Nj7O3tce7cOUKhEHq9XhtOzOVy+Hw+AoGAFkqr1crExASZTIZarYbNZjuz8xU+n48f//jHyLKM1Wqlp6fn2JdfURSCwSDf//73O7ZX5HFdC0Xzi/V4+7B1rFyn02kblZ63Y9W86oTDYQqFAnNzc8eGH5tt7nw+z/DwsFar9vX1EQqFmJ+fZ3x8HJfLpR3P7/fzta99jWAweKzda7PZ8Pl8zM3NMT09rR1Pp9PhcrlYWFjA5/NpcxrwqBl56dIlTCYTAwMDp3aFNJlMhEIh3G63drz+/n4qlQomkwlZljGbzYyOjmo1c7srKbPZTDAYPPG2o83+12uvvUZ/f39bz+VpuhYKo9HI4OAgTqdTu0+S0+mkWq1qzSej0Yjb7cZms51au3Jubg6v18vQ0NCx2n1kZETrDzT7E4A2qnX9+nXGx8ePDQ8Gg0GuX7+Oy+U69uEZDAYGBwe5du0agUDg2BWpr6+PN998k97eXu3L33zt8/PzeL3eU52cslgsXLhwAa/Xq/VDfD6fNponyzJ2u52XXnqJwcHBts4UNzWbyidp9s+aFVCndS0UbrebN954A6PRqA2xzc7OUqvVMBgMGAwGrFYrr7zyCjqd7tTalj6fT+sPPP7BmM1mrRnU+sVo1lqPB6L5GhwOx1Pb61arlYWFhSfO22azMTc3p42UNWvKZp/D5XKd6nCj1Wplfn7+2OagQCBAvV7X3ne73c7s7OwT78mLqmvvgF6vp6+v79jPWjuWsiw/Md/wvJohbNUc6XjaY82Qtmr2E55GluWnLlpr9m2eVv5J5TyP5pXgca2vsdm2Fx4Ri/cFoYUIhSC0EKEQhBYiFILQQoRCEFqIUAhCi7YMyTa3E1arVSqVSjuKOKZSqVCv11+oPc7NHYupVIq9vb2OlFmtVikWix2/cXannXoommvu8/k8BwcH2kb/dioWixSLxRfqLwg1t+zevHmT1dXVjpSpqiq7u7uEw+GOlNct0q9+9avGad5KPhaLEY1GMRqN2n7jdqvVauzv76PX67VlGp24h203rays8OGHH+JwODo6C53P5xkbG+NLX/pSx8pspSgK586dIxgM4vf7T//4kUjkVJs4NpuNUCjE3t4exWLx1I77LJIk4XA4aDQa5HI51tfXz+wK06ZKpUI4HG77vXNb9fX1odfrn3qjsk7R6/VYLBaGhobacnzl9ddfP9U7dTcXsnWz3fki/Imtbvefuvkey7KMz+fD4/G05fiK1+vt6F/CEYTnpdPpnrpw87Qodrv9zI8mCGdL815Z7RpYEfMUgtBChEIQWohQCEILEQpBaCFCIQgtRCgEoYUIhSC0EKEQhBYiFILQQmn3vf4F4bS1+zsrlUqlF2dnjnBmPH4judMmNbq93FIQ/seIPoUgtBChEIQWIhSC0EKEQhBaiFAIQgsRCkFoIUIhCC1EKAShhQiFILQQoRCEFiIUgtBChEIQWohQCEILEQpBaCFCIQgtRCgEoYUIhSC0EKEQhBYiFILQQoRCEFqIUAhCi/8DJYeBlomoQDsAAAAASUVORK5CYII=)
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,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)
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