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?

विकल्प

• μ < μ', M < M'

• μ > μ', M < M'

• μ < μ', M > M'

• μ > μ', M > M'

Answer 1

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'