Question

A carpet of mass M made of of inextensible material is rolled its length in the form of cylinder of radius R and is kept on the rough floor . The carpet starts unrolling without sliding on the floor when a negligible small force is given to it. calculate the horizontal velocity of the axis of cylinder part of the carpet when its radius reduced to R /2 .​

Answer 1

Answer:

Explanation:

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

Explanation:

Your answer refer in Attachment

Thank you