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Question

A uniform metal rod of length L and mass M is rotating with an angular speed ω about an axis passing through one of the ends and perpendicular to the rod. If the temperature increases by tC, then the change in its angular speed is proportional to


A

ω

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B

ω

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C

ω2

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D

1ω

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Solution

The correct option is B

ω


At tC, the length of the rod becomes L=L(1+αt) where α is the coefficeing of linear expansion.
From the law of conservation of angular momentum we have, Iω=Iω13ML2ω=13ML2ωωω=(LL)2=1(1+αt)2
Now, for a given value of t, (1+at)2 is a constant, say k.
ωω=kωωω=k1ωω=(k1)ω(ωω)ω
Hence, the correct choice is (b).


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