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

Answer

C

Explanation

( c) In cricitcal case, weight of hanging part= force of friction of the part of rope lying on table.
`therefore" " (m)/(l).l_(1)g=(m)/(l)(l-l_(1))g`
Solving this we get,
`l_(1)=((mu)/(1+mu))l`