Question

# A rigid spherical body is spinning around an axis without any external torque. Due to temperature its volume increases by 3%. Then percentage change in its angular speed is−2%−3%1%−1%

Solution

## The correct option is A −2%The moment of inertia of a solid sphere,  I=25mR2 or  I∝R2 We know that volume =43πR3 i.e.,  V∝R3 or   ΔVV×100=3ΔRR×100 Percentage increase in volume is 3% ∴ Percentage increase in radius will be 1%. ∴ Percentage increase in moment of inertia will be 2%.    As, I∝R2 Now, since angular momentum L=Iω will remain conserved. Hence, the angular velocity ω will decrease by 2% to keep the angular momentum constant. Hence option A is the correct answer

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