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. When released from the initial horizontal position, its instantaneous angular acceleration will be

• A

  $\frac{g}{2l}$
• B

  $\frac{7g}{3l}$
• C

  $\frac{g}{3l}$
• Correct answer
  D

  $\frac{g}{13l}$

Solution

Both the weight will produce torques in opposite directions,

 ${\tau }_{\mathrm{net}}=I\mathrm{\alpha }$ (where $I\to$moment if inertia about axis of rotation)

$\left(5mg\right)l-\left(2mg\right)\left(2l\right)=\left(2m{\left(2l\right)}^2+5m{\left(l\right)}^2\right)\mathrm{\alpha }$

$\mathrm{\alpha }=\frac{g}{13l}$

Hence, the correct answer is option: 'D'.