Question

A carpet of mass $M$ made of inextensible material is rolled along its length in the form of a cylinder of radius $R$ and is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. Loss in potential energy due to unrolling radius changes from $R$ to $\frac{R}{2}$ is

• A. $\frac{7}{8}MgR$
• B. $\frac{8}{7}MgR$
• C. $\frac{2}{5}MgR$
• D. $\frac{1}{2}MgR$

Answer 1

The correct option is A $\frac{7}{8}MgR$

Initial potential energy is given as $MgR$
Potential energy at the final point = $\frac{M}{4}g\frac{R}{2}$=$Mg\frac{R}{8}$(as rollling mass is the quarter fraction of the initial mass)
Thus we get the release in the potential energy as $M-Mg\frac{R}{8}=\frac{7}{8}MgR$