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Length of a chain is L and coefficient o...

Length of a chain is L and coefficient of static fricition is `mu`. Calculate the maximum length of the chain which can be hang from the table without silking.

Text Solution

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Let y be the maximum length of the chain can be hold out side the table without sliding.
Length of chain of the tabel = (L-y)
Weight of part of the chain on table `W'=M/L(L-y)g`
Weight of hanging part of the chain `W=M/Lyg`

For equlibrium : limiting force of friction = weight of hanging part of the chain
`muR=Wimplies" "muW'=W" "impliesmuM/L(L-y)g=M/LygimpliesmuL-muL-muy=yimpliesy=(muL)/(1+mu)`
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