Question

A sphere is moving towards the positive $x$-axis with a velocity $v_c$ and rotates clockwise with angular speed $\omega$ shown in the figure such that $v_c>\omega r$. The instantaneous axis of rotation will be

• A. on point $P$
• B. on point $P^{{}^{\prime }}$
• C. inside the sphere
• D. outside the sphere

Answer 1

The correct option is D outside the sphere

The instantaneous axis of rotation will fall on the outside of the sphere.
Since, in case of pure rotation, the instantaneous axis of rotation will be on the centre.
In case of pure rolling, the instantaneous axis of rotation will be on $P$. But if $v_c>\omega R$, then there will not be any point on or inside the sphere for which the velocity will be zero w.r.t ground, thus the instantaneous axis of rotation will fall out of the sphere.