A uniform rope of length l lies on a table . If the coefficient of friction is `mu` , then the maximum length `l_(1)` of the part of this rope which can overhang from the edge of the table without sliding down is :

Options

A. `(1)/(mu)`
B. `(1)/(mu + 1)`
C. `(mu l ) /(mu + 1)`
D. `(mu l)/( mu -1)`

Answer

C

Explanation

Let y be the maximum length that can be hanged down the table . For equilibrium ,
Weight of hanging part = Fricti nal force
`((Mg)/(l)) y = mu (M)/(l) (l -y) g`
`y = mu ( l - y)`
` y = (mu l)/(1 + mu)`