A slender uniform rod of length L is balanced | vedclass

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(D) Let the rod have mass $M$ and length $L$. The rod is placed vertically on a horizontal surface with friction. Since the surface has friction,the p

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lies at $P$

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(D) Let the rod have mass $M$ and length $L$. The rod is placed vertically on a horizontal surface with friction. Since the surface has friction,the point of contact $P$ remains stationary as the rod falls. There are no external horizontal forces acting on the rod-surface system in the horizontal direction (assuming the friction is sufficient to prevent slipping). According to the principle of conservation of momentum,the horizontal position of the centre of mass $(CM)$ of the rod remains unchanged. Initially,the rod is vertical,so its $CM$ is directly above the point of contact $P$. Therefore,the horizontal coordinate of the $CM$ is at $P$. When the rod becomes horizontal,its $CM$ must still be at the same horizontal position as it was initially. Thus,the $CM$ lies at $P$.

$A$ slender uniform rod of length $L$ is balanced vertically at a point $P$ on a horizontal surface having some friction. If the top of the rod is displaced slightly to the right,the position of its centre of mass at the time when the rod becomes horizontal is:

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