There block A B ,and C of equal mass `m` are placed one over the other on a frictionless surface (table) as shown in figure The coefficient of friction between any blocks A ,B and C is `mu` The maximum value of mass of block D so that the blocks A,B and C move without slipping over each other is

Options

A. `(3 m mu)/(mu + 1)`
B. `(3 m(1 - mu))/(mu)`
C. `(3 m(1 + mu))/(mu)`
D. `(3 m mu)/((1 - mu)`

Answer

d

Explanation

Maximum acceleration of B of C can be `mg `so that they do not slip with each other or A
For the system of `(A + B+ C)`
`T = 3 ma = 3mu mg`
For D
`Mg - T = Ma`
`rArr Mg - 3mu mg = M mu g`
`rArr M = (3 mu m)/(1 - mu)`