Rotational Motion

JEE Main level, single correct, medium

182 of 280

Question 182 of 280

A slender uniform rod of mass MM and length ll is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ\theta with the vertical is:

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Answer: (B) 3g2lsin⁡⁡θ\dfrac{3g}{2l}\sin ⁡\theta

Moment of a force about OO is lα=mgl2sinθl\alpha =mg\dfrac{l}{2}sin\theta

⇒α=mgl2ml23sin⁡θ\Rightarrow \alpha =\dfrac{mgl}{\dfrac{2m{l}^{2}}{3}}\sin \theta

⇒α=3g2lsin⁡⁡θ\Rightarrow \alpha =\dfrac{3g}{2l}\sin ⁡\theta

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