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Question

In the given figure, an L-shaped frame is free to rotate in a vertical plane about a horizontal axis passing through a smooth hinge O. Each side of the frame has a length L and mass M. The frame is allowed to fall, with one side horizontal and the other vertical.


The linear speed of end A just before striking the ground is

A
3gL10(53)
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B
3gL10(5+3)
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C
3g10L(53)
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D
3g10L(5+3)
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Solution

The correct option is A 3gL10(53)
Initial
Final:

Let ω be the angular speed of point A just before hitting the ground.
Decrease in P.E = Increase in Rotational K.E

Mg[L2L4]+Mg[L3L4]=12IOω2)

IO=IOA+IAB
IOA=ML23

Using parallel axis theorem:

IAB(about O)=[ML212+M(5L2)2]=4ML23
IO=5ML23

So,MgL4(53)=125ML23ω2

On solving the above equation we get:
ω=3g10L(53)
VA=ω(OA)=ωL=3g10L(53)×L=3gL10(53)

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