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. \(\sqrt{2gL}\) \(sin 60^\circ\)

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?

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. \(\sqrt{ g R}\)$\mathrm{}$