The minimum speed that a simple pendulum's bob should be given so that it rises to a level where its string makes $$60^\circ$$ with the vertical is:

1. $$\sqrt{2gL}$$
2. $$\sqrt{2gL}$$ $$cos 60^\circ$$
3. $$\sqrt{2g(L-L~cos60^\circ)}$$
4. $$\sqrt{2gL}$$ $$sin 60^\circ$$

Subtopic: Â Gravitational Potential Energy |
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Two inclined frictionless tracks, one gradual and the other steep meet at $$A$$ from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

 1 Both stones reach the bottom at the same time but not at the same speed. 2 Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II. 3 Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I. 4 Both stones reach the bottom at different times and at different speeds.

Subtopic: Â Gravitational Potential Energy |
Â 62%
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A gravitational field is present in a region and a mass is shifted from $$A$$ to $$B$$ through different paths as shown. If $$\mathrm{W_1}$$, $$\mathrm{W_2}$$ and $$\mathrm{W_3}$$ represent the work done by the gravitational force along their respective paths, then:
 1 $$\mathrm{W}_1=\mathrm{W}_2=\mathrm{W}_3$$ 2 $$\mathrm{W}_1>\mathrm{W}_2>\mathrm{W}_3$$ 3 $$\mathrm{W}_1>\mathrm{W}_3>\mathrm{W}_2$$ 4 $$\mathrm{W}_1<\mathrm{W}_2<\mathrm{W}_3$$
Subtopic: Â Gravitational Potential Energy |
Â 85%
From NCERT
NEET - 2022
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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. $$\sqrt{2 g R}$$
2. $$\sqrt{3 g R}$$
3. $$\sqrt{5 g R}$$
4. $$\sqrt{ g R}$$

Subtopic: Â Gravitational Potential Energy |
Â 85%
From NCERT
NEET - 2016
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