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Question
A boy of mass M is applying a horizontal force to slide a box of mass M' on a rough horizontal surface. The coefficient of friction between the shoes of the boy and the floor is μ and that between the box and the floor is μ'. In which of the following cases it is certainly not possible to slide the box?
Options
μ < μ', M < M'
μ > μ', M < M'
μ < μ', M > M'
μ > μ', M > M'
Solution
μ < μ', M < M'
Let T be the force applied by the boy on the block. 
Free body diagram for the box:
The condition for preventing the slide is
fmax > T
μ'M'g > T (i)
Now see the free body diagram of a boy of mass M:
fmax = μmg
The condition for preventing the slide is
fmax > T
μmg > T
The condition for sliding the entire system (block and boy) is
f' > f (block is not slide)
μ'M'g > μmg
μ'M' > μm
μ < μ'
m < M'
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