Q.

A small sphere of mass m is suspended from a fringe by a light rigid rod of length l. The rod can swing in a vertical circle with what minimum velocity should the sphere be projected horizontally for which it will complete a vertical revolution ?

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a

5gl

b

gl2

c

2gl

d

gl

answer is C.

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Detailed Solution

(3)For the minimum velocity of projection, the velocity of projection at the top most position of its trajectory will be zero.Conserving Energy,  12m  umin2  +  0=0+mg  .  2l⇒    umin  =  2gl
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A small sphere of mass m is suspended from a fringe by a light rigid rod of length l. The rod can swing in a vertical circle with what minimum velocity should the sphere be projected horizontally for which it will complete a vertical revolution ?