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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 ?

a
5gl
b
gl2
c
2gl
d
gl

detailed solution

Correct option is C

(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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Similar Questions

Directions : These questions consist of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses 

Assertion: One end of a massless rod of length l is hinged, so that it is free to rotate in a vertical plane about a horizontal axis. If a particle is attached to the other end of the rod, then the minimum speed at  lower most position of the particle is 5gl to
complete the circular motion. 
Reason : Work done by centripetal force on the particle is always zero.


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