System Of Particles And Rotational Motion Ques 29

29. $A$ rod $P Q$ of mass $M$ and length $L$ is hinged at end $P$. The rod is kept horizontal by a massless string tied to point $Q$ as shown in figure. When string is cut, the initial angular acceleration of the rod is

[2013]

(a) $g/L$

(b) $2g/L$

(c) $2g/3L$

(d) $3g/2L$

Show Answer

Answer:

Correct Answer: 29.(d)

Solution:

  1. (d)

Weight of the rod will produce the torque

$\tau=mg \frac{L}{2}=I \alpha=\frac{mL^{2}}{3} \alpha \quad [\because I _{\text{rod }}=\frac{ML^{2}}{3}]$

Hence, angular acceleration, $\alpha=\frac{3 g}{2 L}$

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