A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

A body initially at rest and sliding along a frictionless track from a height \(h\) (as shown in the figure) just completes a vertical circle of diameter \(\mathrm{AB}= D.\) The height \({h}\) is equal to:
        
1. \({3\over2}D\)
2. \(D\)
3. \({7\over4}D\)
4. \({5\over4}D\)

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. \(\sqrt{ g R}\)$\mathrm{}$

A ball is thrown vertically downward from a height of \(20\) m with an initial velocity \(v_0\). It collides with the ground, loses \(50\%\) of its energy in a collision, and rebounds to the same height. The initial velocity \(v_0\) is: 
(Take, \(g=10~\mathrm{ms^{-2}}\))
1. \(14\) ms^–1
2. \(20\) ms^–1
3. \(28\) ms^–1
4. \(10\) ms^–1