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

f_{max} > T

μ'M'g > T (i)

Now see the free body diagram of a boy of mass M:

f_{max} = μmg

The condition for preventing the slide is

f_{max} > 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'