A cylinder is kept vertical on a horizontal surface. A chain of length ‘ 
R’ and mass ‘M’ placed touching the cylinder as shown in figure. The chain is pulled by a horizontal force so that it is moving very slowly with constant speed ‘v 0 ’. Friction coefficient between cylinder and chain is ‘µ’ while there is no friction between chain and the surface. Then by time chain is completely pulled off the cylinder –
µMv 2
Text Solution
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(a, b)
Friction acts on the part of chain which is in contact with cylinder.
Let ‘x’ part of chain is pulled out at any instant
Friction force on chain = 
W f = 
.dx = 
Heat generated = – W f = 
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