Question

The figure shows a system consisting of (i) a ring of outer radius $3R$ rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius $2R$ rotating anti-clockwise with angular speed $\omega /2$. The ring and disc are separated by frictionless ball bearings. The point $P$ on the inner disc is at a distance $R$ from the origin, where $OP$ makes an angle of ${30}^{\circ }$ with the horizontal. Then with respect to the horizontal surface.

• A. The point $O$ has linear velocity $3R\omega \hat{i}$
• B. The point $P$ has linear velocity $\frac{11}{4}R\omega \hat{i}+\frac{\sqrt{3}}{4}R\omega \hat{k}$
• C. The point $P$ has linear velocity $\frac{13}{4}R\omega \hat{i}-\frac{\sqrt{3}}{4}R\omega \hat{k}$
• D. The point $P$ has linear velocity $(3-\frac{\sqrt{3}}{4})R\omega \hat{i}+\frac{1}{4}R\omega \hat{k}$

Answer 1

Answer: (A), (B)

The correct options are
A The point $O$ has linear velocity $3R\omega \hat{i}$
B The point $P$ has linear velocity $\frac{11}{4}R\omega \hat{i}+\frac{\sqrt{3}}{4}R\omega \hat{k}$