The temperature of a thin uniform rod increase by Δt If moment of intertia 1 about an axis perpendicular to its length then its moment of increase by
A
0
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B
αIΔt
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C
2αIΔt
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D
α2IΔt
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Solution
The correct option is C2αIΔt Given - ∗ Temperatwe of Rod increased by Δt Let the Length of the Rod be (L) and its coefficient of linear expansion be ( α ) Therefore its change in Length will be ΔL=L0⋅αΔt
we have moment of Inertia of Rod about its centre perpendicular to its Length =II=ML212
⇒ By Error analysis we get- ΔII=2ΔLLΔI= change in moment of Inertia
⇒ΔI=2ΔLL0⋅IΔI=2(L0αΔt)L0⋅I=2αIΔtΔI=2αIαt Hence, option (C) is correct.