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A carpet of mass M is rolled along its l...

A carpet of mass `M` is rolled along its length so as to from a cylinder of radius `R` and is kept on a rough floor. When a negligibly small push is given to the cylindrical carpet, it stars unrolling itself without sliding on the floor. Calculate horizontal velocity of cylindrical part of the carpet when its radius reduces to `R//2`.

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To solve the problem, we will use the principles of conservation of energy and the relationship between translational and rotational motion for a rolling object. ### Step-by-Step Solution: 1. **Understanding the System:** - We have a carpet of mass \( M \) rolled into a cylinder of radius \( R \). - When the radius reduces to \( \frac{R}{2} \), we need to find the horizontal velocity \( V \) of the cylindrical part. ...
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