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A uniform rope of length l lies on a tab...

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 :

A

`(1)/(mu)`

B

`(1)/(mu + 1)`

C

`(mu l ) /(mu + 1)`

D

`(mu l)/( mu -1)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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Knowledge Check

  • A uniform rope of length l lies on a table. If the coefficient of friction is mu , then the maximum length L of the part of this rope which can overhang from the edge of the table without sliding down is

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

  • A uniform rope of length l lies on a table if the coefficient of friction is , then the maximum length l, of the part of this rope which can over hang from the edge of the table without sliding down is -

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

  • A uniform rope of length L meters is lying over a table. If the coefficient of friction be mu , then the maximum length L_(1) of the part of the rope which can overhang the edge without sliding is

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

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