Uniform rope of length Tlies on a table with coefficient of friction between the rope and table being u. What is the maximum length of the rope which can over hang from the edge of the table without sliding down?

Options

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

Answer

c

Explanation

Let x be the length hanging and `(l-x)` lying on the surface. Let m be the mass PER UNIT length of the rope. Then the rope will be at the point of sliding when weight of the hanging portion is just equal to the force of friction between surface and rope. Thus
`m (l-x) gmu = mx.g
or mul-mu x = x`
or`x=(mul)/(mu+1)`
Hence correct choice is (c). 37. The block will move if mg sin is greater than or equal to force of friction.