Three blocks A,B and C of equal mass m are placed one over the other on a smooth horizontal ground as shown in figure. Coefficient of friction between any two blocks of A,B and C is 1/2. the maximum value of mass of block D so that the blocks A,B and C move without slippping over each other is

Options

A. (a)6m
B. (b)5m
C. (c)3m
D. (d)4m

Answer

C

Explanation

`f_("max")` between A and B is mg/2, can provide acceleration = g//2 to A and `f_("max")` between B and C is 2mg/2, can provide acceleration = g to c
`implies` max acceleration if they move together as on body = g/2
`implies T = 3m. (g)/(2)` and `Mg - T = (Mg)/(2) implies M = 3m`