An impulsive force F acts horizontally on a solid sphere of radius R placed on a horizontal surface. The line of action of the impulsive force is at a height h above the centre of the sphere. If the r

Question

An impulsive force F acts horizontally on a solid sphere of radius R placed on a horizontal surface. The line of action of the impulsive force is at a height h above the centre of the sphere. If the rotational and translational kinetic energies of the sphere just after the impulse are equal, then the value of h will be-

Assume the horizontal surface is smooth (no tangential impulse from the ground).

TestHub · Accepted Answer

Let the impulse be J; the smooth ground gives no tangential impulse.

$v = \frac{J}{M}, ω = \frac{J h}{I}, I = \frac{2}{5} M R^{2}$

Equal kinetic energies give:

$\frac{J ^{2}}{2 M} = \frac{J ^{2} h ^{2}}{2 I}$

$h = \frac{I}{M} = \frac{2}{5} R$

Answer C.

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2027 (Class 12+)