State of the sphere at some instant of time is shown in figure. Surface below the sphere is rough. At the given instant, speed of the centre of the sphere is u and angular velocity about the centre is u/2r. Select correct statement (s)

Options

A. Direction of friction on the sphere is towards left
B. Direction of friction on the sphere is towards right
C. Angular momentum about point o remains conserved
D. Angular momentum about point B remains conserved

Answer

A, D

Explanation

Forces acting on the sphere are as shown in figure.
Velocity of the bottom point B due to translation is u towards right and due to rotation it is u/2 towards left. Hence net velocity of the bottom point is towards right. So we can understand that friction will act towards eft in order to oppose this relative motion. Option (a) is correct whereas (b) is wrong.
Further we can see that friction is applying torque about the centre O hence angular momentum about the centre will not remain conserved. Hence option (c) is wrong
All the forces are passing through the point B hence there is no torque about this point. So angular momentum about the point B remains conserved. Option (d) is also correct.