Q. No.What is the minimum speed that must be imparted to the bob of a pendulum (at \(A\)), so that it rises to the level of \(O,\) during subsequent motion? The initial position \(A\) and the dimensions are indicated in the figure.
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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The force exerted by the spring equals:
1. \(F\)
2. \(\Large\frac F2\)
3. \(2F\)
4. \(\sqrt2F\)
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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 work done by the force \(F\) equals:
1. \(\dfrac{Fd}{2}\)
2. \(Fd\)
3. \(2Fd\)
4. \(\dfrac{Fd}{3}\)
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