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Q. No.Two identical masses are connected to a spring of spring constant \(k.\) The two masses are slowly moved symmetrically so that the spring is stretched by \(x.\) The work done by the spring on each mass is:
1. \(\dfrac12 kx^2\)
2. \(\dfrac14kx^2\)
3. \(-\dfrac12 kx^2\)
4. \(-\dfrac14kx^2\)
Subtopic: Â Elastic Potential Energy |
From NCERT
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A small block of mass '\(m\)' is placed against a compressed spring, of spring constant \(k\). The initial compression in the spring is '\(d\)'. The block is released and the spring relaxes, while the block is projected up to a height \(H\) relative to its initial position. Then, \(H\) =
| 1. | \(\dfrac{kd^2}{2mg}\) | 2. | \(\dfrac{kd^2}{2mg}+d \) |
| 3. | \(\dfrac{kd^2}{2mg}-d\) | 4. | \(\dfrac{kd^2}{mg}+d\) |
Subtopic: Â Elastic Potential Energy |
From NCERT
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A block is suspended from a spring and causes an extension of \(2\) cm. It is now imparted a kinetic energy \(E\) so that the block rises up by exactly \(2\) cm. If the block were to be given the same kinetic energy upward, without being attached to a spring, it would rise up by:
1. \(1\) cm
2. \(2\) cm
3. \(4\) cm
4. \(8\) cm
1. \(1\) cm
2. \(2\) cm
3. \(4\) cm
4. \(8\) cm
Subtopic: Â Elastic Potential Energy |
From NCERT
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In the figure, the coefficient of friction between the block (mass \(m\)) and the horizontal surface is \(\mu\). The block is given an initial velocity to the left compressing the spring by \(x_1\). The block 'rebounds' and then the spring gets extended - the maximum extension being \(x_2\).
| 1. | \(x_{1}+x_{2}=\dfrac{\mu m g}{k}\) |
| 2. | \(x_{1}-x_{2}=\dfrac{\mu m g}{k}\) |
| 3. | \(x_{1}+x_{2}=\dfrac{2\mu m g}{k}\) |
| 4. | \(x_{1}-x_{2}=\dfrac{2\mu m g}{k}\) |
Subtopic: Â Elastic Potential Energy |
From NCERT
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One end of the vertical spring is fixed to the ground, while the other end is connected to a ring of mass \(m,\) that can slide on a fixed smooth horizontal rod. The ring is given a velocity \(v\) so that it moves to the right up to a distance \(h,\) the length of spring in its initial unextended position. The speed \(v\) equals:
| 1. | \(\sqrt{\dfrac{kh^2}{m}} \) | 2. | \(\sqrt{\dfrac{k(\sqrt2-1)h^2}{m}} \) |
| 3. | \((\sqrt2+1)\sqrt{\dfrac{kh^2}{m}} \) | 4. | \((\sqrt2-1)\sqrt{\dfrac{kh^2}{m}}\) |
Subtopic: Â Elastic Potential Energy |
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