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A rigid rod of mass m & length l is pivo...

A rigid rod of mass m & length l is pivoted at one of its ends. If it is released from its horizontal position, find the speed of the centre of mass of the rod when it becomes vertical.

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To find the speed of the center of mass of a rigid rod of mass \( m \) and length \( l \) when it is released from a horizontal position and becomes vertical, we can use the work-energy theorem. Here’s a step-by-step solution: ### Step 1: Understand the System The rod is pivoted at one end and is initially horizontal. When released, it rotates about the pivot due to the gravitational force acting on it. ### Step 2: Identify the Work Done by Gravity The work done by gravity as the rod moves from the horizontal to the vertical position can be calculated. The center of mass of the rod is located at a distance of \( \frac{l}{2} \) from the pivot. ...
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