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 .
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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
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