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JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Rotational Mechanics

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A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ______ .

Answer: 6

Solution

Take the rotation to be about the clamped lower end, for which the rod's moment of inertia is . As the rod swings from pointing straight up to its lowest position, pointing straight down, its centre of mass descends through the full length . Energy conservation then reads , so . The speed of the free end is .

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Integer answer

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