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.

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.

Tardigrade Admin · Accepted Answer

The kinetic energy of a rolling solid sphere

= k_{trans} + k_{rot}

= \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}

= \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{5} m R^{2} ω^{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.

Q. 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.

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

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

Assertion is true but reason is false.

Both assertion and reason are false.

The kinetic energy of a rolling solid sphere =ktrans ​+krot ​ =21​mv2+21​Iω2 =21​mv2+21​×52​mR2ω2 =21​mv2+51​mv2 =7/10mv2 Different solid bodies have different kinetic energy as for different solid bodies, I is different.

Q. 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.