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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 ?
Angular velocity
Angular momentum
Moment of inertia
Rotational kinetic energy
- Increasing the radius of the sphere while keeping the mass constant will increase its moment of inertia. This is because the mass distribution is now further from the axis of rotation.
- Angular momentum is given by the product of moment of inertia and angular velocity. In the absence of external torques, this quantity is conserved. Hence, increasing the radius does not affect it.
- Angular velocity will decrease as a result of the increased moment of inertia, due to the conservation of angular momentum.
- Moment of inertia will change because it is dependent on the radius; a larger radius increases it.
- Rotational kinetic energy depends on both moment of inertia and angular velocity. Since both change to conserve angular momentum, the kinetic energy will be affected.
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