Q. No.A simple pendulum consisting of a bob of mass \(m\), and a string of length \(L\) is given a horizontal speed \(u\), at its lowest point as shown in the figure. As a result, it rises to \(B\), where it just comes to rest momentarily with \(OB\) horizontal. During the motion \(AB\text:\)
| 1. | Work done by the string is zero |
| 2. | Work done by gravity is \(-mgL\) |
| 3. | Change in K.E. of the bob is \(-\dfrac{1}{2}mu^2\) |
| 4. | All the above are true |
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 gR}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{g R}\)
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
NEET - 2016
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A body is falling freely under the action of gravity alone in a vacuum. Which of the following quantities remain constant during the fall?
| 1. | kinetic energy |
| 2. | potential energy |
| 3. | total mechanical energy |
| 4. | total linear momentum |
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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A simple pendulum of length \(1~\text{m}\) has a bob of mass \(1~\text{kg}.\) The bob is held horizontally (so the string is horizontal) and then released from rest. Taking \(g=10~\text{m/s}^2,\) what is its speed at the lowest point?
| 1. | \(2\sqrt{10}\) ms–1 | 2. | \(2\sqrt{5}\) ms–1 |
| 3. | \(4\sqrt{10}\) ms–1 | 4. | \(4\sqrt{5}\) ms–1 |
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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When a projectile is projected under a uniform gravitational field (air resistance is negligible):
| 1. | Its kinetic energy is conserved. |
| 2. | Its potential energy is conserved. |
| 3. | The sum of potential and kinetic energies is conserved. |
| 4. | Energy conservation is not valid for projectile motion. |
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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A particle of mass \(1~\text{kg}\) starts from rest at point \(A,\) which is \(2~\text m \) above a reference level and slides down a frictionless track \(AOC.\) After passing point \(C\), it leaves the track and moves freely as a projectile. When the particle reaches its highest point \(P\) during its flight, its height is \(1~\text m \) above the reference. What is the kinetic energy of the particle at point \(P\text{?}\) \((\text{use}~g=10~\text{m/s}^{2})\)
1. \(10~\text J\)
2. \(20~\text J\)
3. \(30~\text J\)
4. \(40~\text J\)
1. \(10~\text J\)
2. \(20~\text J\)
3. \(30~\text J\)
4. \(40~\text J\)
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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In a simple pendulum of length \(10 ~\text m,\) the string is initially kept horizontal and the bob is released. \(10\%\) of energy is lost till the bob reaches the lowermost position. The speed of the bob at the lowermost position is:
1. \(6~\text{m/s}\)
2. \(6\sqrt5~\text{m/s}\)
3. \( 7\sqrt5~\text{m/s}\)
4. \(4\sqrt2~\text{m/s}\)
1. \(6~\text{m/s}\)
2. \(6\sqrt5~\text{m/s}\)
3. \( 7\sqrt5~\text{m/s}\)
4. \(4\sqrt2~\text{m/s}\)
Subtopic: Conservation of Mechanical Energy |
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An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?
1. momentum
2. potential energy
3. acceleration
4. force
1. momentum
2. potential energy
3. acceleration
4. force
Subtopic: Conservation of Mechanical Energy |
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A stone tied to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u.\) The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{{x}\left({u}^2-{gL}\right)} .\) The value of \(x\) is:
1. \(3\)
2. \(2\)
3. \(1\)
4. \(5\)
1. \(3\)
2. \(2\)
3. \(1\)
4. \(5\)
Subtopic: Conservation of Mechanical Energy |
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Level 2: 60%+
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Given below are two statements:
| Assertion (A): | According to the law of conservation of mechanical energy change in potential energy is equal and opposite to the change in kinetic energy. |
| Reason (R): | Mechanical energy is not a conserved quantity. |
| 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. |
Subtopic: Conservation of Mechanical Energy |
82%
Level 1: 80%+
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