Q. No.A block is connected to a wall by an elastic spring, which is initially unextended. A constant force \(F\) is applied to the block, so that the spring is stretched and the block moves to the right. The spring extends and slows the block down, and it comes to rest again, briefly. There is no friction anywhere. The displacement of the block is \(d.\)
The work done by the force \(F\) equals:
1. \(\dfrac{Fd}{2}\)
2. \(Fd\)
3. \(2Fd\)
4. \(\dfrac{Fd}{3}\)
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The potential energy stored in the spring equals:
| 1. | \(\Large\frac{Fd}{2}\) | 2. | \(Fd\) |
| 3. | \(\Large\frac{2Fd}{3}\) | 4. | \(\Large\frac{Fd}{3}\) |
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The force exerted by the spring equals:
1. \(F\)
2. \(\Large\frac F2\)
3. \(2F\)
4. \(\sqrt2F\)
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| 1. | \(\sqrt{gL}\) | 2. | \(\sqrt{\Large\frac{gL}{2}}\) |
| 3. | \(\sqrt{2gL}\) | 4. | \(\sqrt{\Large\frac{5gL}{2}}\) |
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| Assertion (A): | Work done by all forces, conservative or non-conservative, equals the change in the total energy of the system. |
| Reason (R): | According to Newton's laws of motion, the acceleration of any particle of the system is due to all forces acting on it; and therefore the work done on it by these is the total work done. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
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| 1. | \(\dfrac{1}{2}\) | 2. | \(\dfrac{1}{3}\) |
| 3. | \(\dfrac{1}{9}\) | 4. | \(\dfrac{1}{\sqrt3}\) |
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1. \(mgh\)
2. \(\Large\frac{mgh}{2}\)
3. \(-mgh\)
4. zero
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1. \({\Large\frac12}\)
2. \({\Large\frac{1}{\sqrt2}}\)
3. \({\Large\frac14}\)
4. \(\sqrt2-1\)
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1. \(E_1=E_2\)
2. \(E_1=2E_2\)
3. \(2E_1=E_2\)
4. \(E_1=4E_2\)
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1. \(20~\text J\)
2. \(19~\text J\)
3. \(21~\text J\)
4. \(42~\text J\)
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