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Question

A rod OA of mass m and length L is rotating in a horizontal circle about point O as shown in figure. B is the mid-point of rod. If T represents tension in the rod at any point and Uo represents elastic strain energy stored in the rod OA, UB represents elastic strain energy stored in the rod (OB) then choose correct alternative (s).

A
To=43TB
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B
To=2TB
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C
Uo=1611UB
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D
Uo=4UB
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Solution

The correct option is C Uo=1611UB
At fixed end,
To=12mω2L
At x, from fixed end
T=12mω2L(L2x2)


At B,
TB=12mω2L(L2L24)TB=38mω2L

i.e., To=43TB
Again, T=12mω2L(L2x2)
Elastic strain energy
dU=12mω2L(L2x2)dx
U=12mω2LL0L2dxL0x2dx=12mω2L(xL2x33)
For OA,x=L
Uo=13mω2L2
and for OB,x=L2
UB=12mω2L(L32L324)=mω2L11L348
i.e., Uo=1611UB

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