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

Options

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

Answer

A

Explanation

Let m: mass of chain
The chain will remain at rest , if
`(m)/(L) L_(1) g le f_(max) [ = mu N = mu (m)/(L) (L - L_(1))g]`
`L_(1) le mu(L - L_(1))`
`L_(1) (mu + 1)le mu L`
`L_(1) le (mu L)/(mu + 1)`
`(L_(1))_(max) = (mu L)/(mu +1)`
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