Question 10: Centre of Mass and Rotational Motion

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.

Accepted Answer

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

Answer

Both assertion and reason are true and reason is the correct explanation of assertion

Answer

Both assertion and reason are true but reason is not the correct explanation of assertion

Answer

Assertion is true but reason is false

Answer

Both assertion and reason are false.

Centre of Mass and Rotational Motion

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.

Choose the correct answer: