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 [NEET 2013]

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

\[Mg\frac{L}{2}=\frac{M{{L}^{2}}}{3}\alpha \]

\[\therefore \]      \[\alpha =\frac{3g}{2L}\]