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Question

# Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in the figure. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7. What is the maximum horizontal force F that can be applied to block M so that both the blocks move together?

A

4 N

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B

16 N

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C

24 N

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D

96 N

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Solution

## The correct option is D 96 N The only horizontal force acting on mass m is the force of friction f. f=μmg=0.5×3×10=15 N This force can produce an acceleration in block m given by a=fm=153=5 m/s2 So, for the blocks to move together, they should have this common acceleration of 5 m/s2. Now, F−f′=(m+M)a⇒F−μ′(m+M)g=(m+M)a⇒F−0.7×(3+5)×10=(3+5)×5⇒F−56=40⇒F=96 N Hence, the correct choice is (d).

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