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Question

A weightless rod of length 2l carries two equal masses ā€²mā€², one secured 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 :
1302900_dc965c0515a04d62aa2fc9d74226b749.png

A
48gl5
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B
64gl5
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C
72gl5
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D
120gl5
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Solution

The correct option is A 48gl5
Energy conservation
12mva2+12mv2b=2Lmg+4Lmg
va2L=vbLva=2vb
and substituting
12mv2a+12m(va2)2=6Lmg
and finally
va=435Lg or 485Lg

1239072_1302900_ans_e7a2671726ea4471a401dc27da8b6577.png

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