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Question

A weightless rod of length 2l carries two equal masses m, one second at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. What horizontal velocity must be imparted to the mass at A so that it just completes the vertical circle.
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A
485gl
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B
455gl
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C
405gl
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D
355gl
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Solution

The correct option is A 485gl
From Law of Conservation of energy potential energy = Kinetic Energy
4 mgl+2 mgl=mv2B2+mv2A2
The angular velocity at point A and B are same
Va2L=VbLVs=2Vb
6 mgl=12mv2a+12mV2a4
Va=435Lg=485 Lg

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