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 \[\tau =l\alpha \] From Eqs. (i) and (ii), we get \[Mg\frac{L}{2}=\frac{M{{L}^{2}}}{3}\alpha \] \[\therefore \] \[\alpha =\frac{3g}{2L}\]