Question

A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:

• A. $\frac{g}{13l}$
• B. $\frac{g}{3l}$
• C. $\frac{g}{2l}$
• D. $\frac{7g}{3l}$

Answer 1

The correct option is A $\frac{g}{13l}$

Applying torque equation about point $P$

$\tau =I\alpha =\left[2M_0\right(2l{)}^2+5M_0{l}^2]\alpha$
$\Rightarrow 5M_{0}gl-4M_{0}gl=\left[2M_0\right(2l{)}^2+5M_0{l}^2]\alpha$
$\Rightarrow 5M_{0}gl=\left(13M_{0}g{l}^2\right)\alpha$
$\therefore \alpha =\frac{g}{13l}$.