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 `(r)/(2)` without sliding is (g =acceleration due to gravity)

Options

A. `(3)/(4) mgr`
B. `(5)/(8) mgr`
C. `(7)/(8) mgr`
D. `(1)/(2) mgr`

Answer

C

Explanation

Mass left over unrolled `= (m)/(pi r^(2)) xx pi ((r)/(2))^(2)= (m)/(4)`
decrease in P.E. `= mgr- ((m)/(4))g (r)/(2)= (7)/(8) mgr`