Question

Assertion The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.
Reason For all solid bodies, total kinetic. energy is always twice of translational kinetic energy.

• A. Both assertion and reason are true and reason is the correct explanation of assertion
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false.
• D. Both assertion and reason are false.

Answer 1

Answer: (C)

The kinetic energy of a rolling solid sphere
$=k_{\text {trans }}+k_{\text {rot }}$
$=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}$
$=\frac{1}{2} m v^{2}+\frac{1}{2} \times \frac{2}{5} m R^{2} \omega^{2}$
$=\frac{1}{2} m v^{2}+\frac{1}{5} m v^{2}$
$=7 / 10\, m v^{2}$
Different solid bodies have different kinetic energy as for different solid bodies, $I$ is different.