Q.

Three blocks 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 μ. The maximum value of mass of block D so that the blocks A, B, and C move without slipping over each other is

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a

3μ+1

b

3m(1μ)μ

c

3m(1+μ)μ

d

3(1μ)

answer is D.

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Detailed Solution

Maximum acceleration of B or C can be mg so that they do not slip with each other or on A. 

For the system of (A+B+C):

         T=3ma=3μmg

For D:

            MgT=Ma     Mg3μmg=Mμg     M=3μm1μ

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