Question

A uniform rod $A B$ of length $\ell$ and mass $m$ is free to rotate about point $A .$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{m \ell^{2}}{3}$, the initial angular acceleration of the rod will be:-

• A. $mg \frac{\ell}{2}$
• B. $\frac{3}{2} g \ell$
• C. $\frac{3 g}{2 \ell}$
• D. $\frac{2 g}{3 \ell}$

Answer 1

The Correct Option is C

$\because \tau= I \alpha $
$\therefore( mg ) \frac{\ell}{2}=\left(\frac{ m \ell^{2}}{3}\right) \alpha $
$\Rightarrow \alpha=\frac{3 g }{2 \ell}$