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].