question_answer

A uniform rod AB of mass m and length la is falling freely without rotation under gravity with AB horizontal. Suddenly the end A is fixed when the speed of the rod is v. The angular speed with which the rod begins to rotate is

A) \[\frac{v}{2a}\]                                  

B)  \[\frac{4v}{3a}\]

C) \[\frac{v}{3a}\]                                  

D)  \[\frac{3v}{4a}\] 

Correct Answer: D

Solution :

Angular momentum about A will be conserved, i.e., \[{{L}_{i}}={{L}_{f}}\] \[mva=I\omega \]or \[mva=\frac{m{{(2a)}^{2}}}{3}\omega \]\[\therefore \]\[\omega =\frac{3v}{4a}\] Hence, the correction option is [d].