Question

A uniform rod of mass m and length l is suspended by two strings at its ends as shown.When one of the string is cut,the rod starts falling with an initial angular acceleration

• A. $\frac{3g}{l}$
• B. $\frac{g}{2l}$
• C. $\frac{3g}{2l}$
• D. $\frac{3g}{4l}$

Answer 1

The correct option is A $\frac{3g}{l}$

When the string is wt,the torque acting on the rod due to gravity is:

$\tau =rF\sin \theta$

$=mgl\sin \theta ,\theta =90°$

$\tau =mgl$

Moment of inertia of rod about an axis passing though one end is

$I=\frac{m{l}^2}{3}$

$\alpha =\frac{\tau }{I}=\frac{mgl}{m{l}^2}\times 3=\frac{3g}{l}$