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 kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius r2 without sliding is (g= acceleration due to gra

Answer 1

The volume of the rolled cylindrical carpet = πr²l

=> density = m/πr²l

when the carpet unrolls to a radius of r/2

volume = πr²l/4

Hence its mass

m₁ = density x volume

= m/πr²l  x  πr²l/4

=> m₁ = m/4

Potential energy of the rolled carpet = mgr

potential energy of the half unrolled carpet = m₁g(r/2)

= m/4  x g  x r/2 =  mgr/8

Hence loss in potential energy

= mgr - mgr/8

= 7mgr/8

Hence the decrease in potential energy will be 7mgr/8

Answer 2

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