A uniform chain of mass m and length I is kept on the table with a part of it overhanging (see figure). If the coefficient of friction between the table and the chain is `1//3` then find the maximum length of the chain that can overhang such that the chain remain in equilibrium.

Options

A. `L//3`
B. `L//2`
C. `L//4`
D. `2L//3`

Answer

C

Explanation

Let x be the length of the overhanging part
`f_(r)=mu[(m)/(L)(L-x)g]`
`T=f_(r)`
`T=(m)/(L)xxg`
`rArr mu((m)/(L))(L-x)g=(m)/(L) g x`
`rArr (1)/(3)(L-x)=x rArr x =(L)/(4)`