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Question

A rod of mass M and length L is standing on frictionless horizontal surface vertically. With slight disturbance it starts to fall. When rod is making angle of 37 with vertical,

A
Speed of center of mass is gL3
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B
Angular velocity of rod is 15g13L
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C
Velocity of center of mass is vertically downwards
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D
Speed of point of contact with ground is 12gL65
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Solution

The correct option is D Speed of point of contact with ground is 12gL65

By conservation of energy,
mgL2(145)=12Iw2

where I=1375mL2 is about IAR

mgL10=12.1375mL2w2

w=15g13L

Since there is no horizontal force COM moves in vertical direction.

and Vcom=rcomωVcom=L2cos53ω=31015gL13

Velocity of point of contact is V=L2sin53ω

V=12gL65

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