question_answer

In the given figure, the sphere rolls without slipping on the plank which is moving with constant velocity \[{{v}_{0}}.\]The radius and angular velocity of the sphere is r and \[\omega \]respectively. The velocity of center of mass of the sphere is:

A) \[{{v}_{0}}+r\omega \]                    

B) \[{{v}_{0}}-r\omega \]          

C)      \[r\omega \]                 

D)      \[{{v}_{0}}\]1                       

Correct Answer: A

Solution :

For pure rolling motion of sphere relative motion of Point of contact of sphere and plank should be zero. For this, the point of contact has a velocity equal to the velocity of plank. \[\therefore \]\[{{v}_{0}}={{v}_{CM}}-r\omega \] \[\therefore \]\[{{V}_{CM}}={{v}_{0}}+r\omega \] Hence, the correction option is [a].