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:
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. |
1. | \(W_1=W_2=W_3\) | 2. | \(W_1>W_2>W_3\) |
3. | \(W_1>W_3>W_2\) | 4. | \(W_1<W_2<W_3\) |
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. \(\sqrt{ g R}\)