In the arrangement shown in Fig there is no friction between of mass `2m` and ground but there is friction between the block of masses `m` is stationary with respect to block of mass `2m` The value of friction between `m` and `2m`is

Options

A. `(1)/(2)`
B. `(1)/(sqrt(2)`
C. `(1)/(4)`
D. `(1)/(3)`

Answer

c

Explanation

`f = mA`
`mg - T = mA`…(i)
`T - f = 2mA`….(ii)
`T - f = 2mA`…(iii)
From Eqs (ii) and (iii).
`f = mg//4`
If friction is static, `f le mu mg`
`rArr mu = (1)/(4)`