Question

Select One Correct Option from the following: The figure shows a system consisting of (i) aring of outer radius 3R rolling clockwise with-out slipping on a horizontal surface with angu-lar speed $\omega$ and (ii) an inner disc of radius 2Rrotating anti-clockwise with angular speed $\omega/2$ The ringand disc are separated by frictionlessball bearings. The system is in the x-z plane.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 a linear velocity $3R\omega\hat{i}$.
(B) the point P has a linear velocity $\frac{11}{4} R \omega\hat{i}+\frac{\sqrt{3} }{4} R\omega\hat{k}$.
(C) the point P has a linear velocity $\frac{13}{4} R \omega\hat{i}-\frac{{\sqrt{3} } }{4} R\omega\hat{k}$.
(D) the point P has a linear velocity $\bigg (3-\frac{\sqrt{3}}{4} \bigg ) R \omega\hat{i}+\frac{{{1}}}{4} R\omega\hat{k}$.

Answer 1

c option is correct I think.

Answer 2

Select One Correct Option from the following: The figure shows a system consisting of (i) aring of outer radius 3R rolling clockwise with-out slipping on a horizontal surface with angu-lar speed $\omega$ and (ii) an inner disc of radius 2Rrotating anti-clockwise with angular speed $\omega/2$ The ringand disc are separated by frictionlessball bearings. The system is in the x-z plane.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 a linear velocity $3R\omega\hat{i}$.

(B) the point P has a linear velocity $\frac{11}{4} R \omega\hat{i}+\frac{\sqrt{3} }{4} R\omega\hat{k}$.

(C) the point P has a linear velocity $\frac{13}{4} R \omega\hat{i}-\frac{{\sqrt{3} } }{4} R\omega\hat{k}$.

(D) the point P has a linear velocity $\bigg (3-\frac{\sqrt{3}}{4} \bigg ) R \omega\hat{i}+\frac{{{1}}}{4} R\omega\hat{k}$.