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 .

A carpet of mass M made of of inextensible material is rolled its leng

1.	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» Explanation:The volume of the rolled cylindrical carpet = πr²l=> density = m/πr²lwhen the carpet unrolls to a RADIUS of r/2volume = πr²l/4Hence its massm₁ = density X volume = m/πr²l x πr²l/4=> m₁ = m/4Potential ENERGY of the rolled carpet = mgrpotential energy of the half unrolled carpet = m₁g(r/2)= m/4 x g x r/2 = MGR/8Hence loss in potential energy = mgr - mgr/8= 7mgr/8Hence the decrease in potential energy will be 7mgr/8

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