### Neet Solved Paper 2013 Question 8

##### Question: 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

#### Options:

A) $ \frac{3g}{2L} $

B) $ \frac{g}{L} $

C) $ \frac{2g}{L} $

D) $ \frac{2g}{3L} $

## Show Answer

#### Answer:

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{ML^{2}}{3} $ …(ii)

As $ \tau =la $ From Eqs. (i) and (ii),

we get $ Mg\frac{L}{2}=\frac{ML^{2}}{3}\alpha $

$ \therefore $ $ \alpha =\frac{3g}{2L} $