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A block of mass m is placed on another blocks of mass M which itself is lying on a horizontal surface. The coefficient of friction between the two blocks isµ1 and that between the block of mass M and horizontal surface is pr. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation ?

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a

(M+m)μ2−μ1g

b

(M−m)μ2−μ1g

c

(M−m)μ2+μ1g

d

(M+m)μ2+μ1g

answer is D.

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Detailed Solution

Here the force applied should be such that the force on block of mass m should not exceed from the force of friction (µ1 m g). Let the system move with accelerationa. ThenF−μ2(M+m)g=(M+m)a …(1)For block of mass m,F1=ma=μ1mg or a=μ1g …(2)From eqs. (1) and (2), we getF=μ2(M+m)g+(M+m)μ1g =(M+m)g(μ1+μ2)

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A block of mass m is placed on another blocks of mass M which itself is lying on a horizontal surface. The coefficient of friction between the two blocks isµ1 and that between the block of mass M and horizontal surface is pr. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation ?