JEE Main · 2004 · 24 Apr 2004 · Offline · Rotational Mechanics

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A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

(A)moment of inertia
(B)angular momentum✓ Correct
(C)angular velocity
(D)rotational kinetic energy.

Answer: (B)

Solution

In free space there is no external torque, so the angular momentum is conserved. If the radius grows at fixed mass, the moment of inertia

I = \frac{2}{5} M R^{2}

increases, and since

L = I ω

must hold its value,

ω

falls and the rotational kinetic energy

\frac{1}{2} I ω^{2}

changes along with it. The one quantity that stays fixed throughout is the angular momentum.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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