question_answer

A rod PQ of mass M and length L is hinged at end P. The rod is kepts horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

A) \[\frac{3g}{2L}\]

B) \[\frac{g}{L}\]

C) \[\frac{2g}{L}\]

D) \[\frac{2g}{3L}\]

Correct Answer: A

Solution :

     Torque on the rod=Moment of weight of the rod about P \[\tau =mg\frac{L}{2}\] ?(i) \[\because \]Moment of inertia of rod about \[P=\frac{M{{L}^{2}}}{3}\] ?(ii) As \[\tau =la\] From Eqs. (i) and (ii), we get \[Mg\frac{L}{2}=\frac{M{{L}^{2}}}{3}\alpha \] \[\therefore \] \[\alpha =\frac{3g}{2L}\]