Question 178 of 280

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$\dfrac{g}{2l}$B$\dfrac{7g}{3l}$C$\dfrac{g}{3l}$D$\dfrac{g}{13l}$

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Answer: (D) $\dfrac{g}{13l}$

Both the weight will produce torques in opposite directions,

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

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

$\alpha =\dfrac{g}{13l}$