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Question
If the temperature of a uniform rod is slightly increased by ∆t, its moment of inertia I about a perpendicular bisector increases by
Options
zero
αI∆t
2αI∆t
3αI∆t.
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Solution
2αI∆t
The change in moment of inertia of uniform rod with change in temperature is given by,
I′ =I (1+2∝Δt)
Here, I = initial moment of inertia
I' = new moment of inertia due to change in temperature
∝= expansion coefficient
Δt = change in temperature
So, I′ - I = 2αIΔt
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