question_answer

A uniform solid cylinder rolling with angular velocity \[\omega \] along a plane surface strikes a vertical rigid wall. With what angular velocity the cylinder begins to roll up the wall because of impulsive blow?

A)  \[\frac{\omega }{2}\]                        

B) \[\frac{\omega }{3}\]

C)  \[\frac{\omega }{4}\]                        

D)  \[\frac{\omega }{5}\] 

Correct Answer: B

Solution :

Applying law of conservation of angular momentum about point O \[I\omega =I\omega '+mvR\]or \[\left( \frac{m{{R}^{2}}}{2} \right)\omega =\left( \frac{m{{R}^{2}}}{2} \right)\omega '+m\omega '{{R}^{2}}\] \[=\left( \frac{m{{R}^{2}}}{2}+m{{R}^{2}} \right)\omega '\] \[\therefore \]    \[\omega '=\omega /3\] Hence, the correction option is [b].