A uniform cylinder of radius $r$ and length L and mass $m$ is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is:

m g [(\frac{L}{2}) - r]

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m g [(\frac{g}{2}) - r]

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m (g L - 1)

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M g L r

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Solution

The correct option is A $m g [(\frac{L}{2}) - r]$
Work done=change in potential energy of center of mass
Initially when cylinder is lying with curved surface touching the ground, COM is at height R (R is radius of cylinder)
When it is oriented on the ground with the flat surface touching the ground, COM is at height L/2 (L is length of cylinder)
Change in height of COM is $(\frac{L}{2} - R)$
Change in potential energy $= m g (\frac{L}{2} - R)$
Work done $= m g (\frac{L}{2} - R)$

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A uniform cylinder of radius r and length L and mass m is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is:

A uniform cylinder of radius $r$ and length L and mass $m$ is lying on the ground with the curved surface touching the ground. If it is to be oriented on the ground with the flat circular end in contact with the ground the work to be done is: