A carpet of mass \( m \) made of inextensible material is rolled along its length in the form of...

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A carpet of mass \( m \) made of inextensible material is rolled along its length in the form of a cylinder of radius \( r \) and kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius \( \frac{r}{2} \) without sliding is ( \( g= \) acceleration due to gravity) [Kerala PET 2012]
(a) \( \frac{3}{4} m g r \)
(b) \( \frac{5}{8} m g r \)
(c) \( \frac{7}{8} m g r \)
(d) \( \frac{1}{2} m g r \)
(e) \( \frac{1}{8} m g r \)
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