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Q. No.A bob of heavy mass \(m\) is suspended by a light string of length \(l.\) The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point \(P\) making an angle \(\theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point \(P\) to its initial speed \(v_0\) is:
| 1. | \(\left(\dfrac{\cos \theta}{2+3 \sin \theta}\right)^{-1 / 2}\) | 2. | \(\left(\dfrac{\sin \theta}{2+3 \sin \theta}\right)^{1 / 2}\) |
| 3. | \((\sin \theta)^{1 / 2}\) | 4. | \(\left(\dfrac{1}{2+3 \sin \theta}\right)^{1 / 2}\) |
Subtopic: Â Conservation of Mechanical Energy |
 54%
Level 3: 35%-60%
NEET - 2025
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When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:
1. \(1:2\sqrt{3}\)
2. \(1:\sqrt{2}\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{3}\)
Subtopic: Â Conservation of Mechanical Energy |
 75%
Level 2: 60%+
NEET - 2019
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A ball is dropped from a height of \(5~\text {m}.\) If it rebounds up to a height of \(1.8~\text {m},\) then the ratio of velocities of the ball after and before the rebound will be:
1. \(\dfrac{3}{5}\)
2. \(\dfrac{2}{5}\)
3. \(\dfrac{1}{5}\)
4. \(\dfrac{4}{5}\)
Subtopic: Â Conservation of Mechanical Energy |
 77%
Level 2: 60%+
AIPMT - 1998
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- 1(current)
Q. No.
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