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 given the boy is not slipping

• A. $\mu <{\mu }^{\prime }$ , M<M'
• B. $\mu >{\mu }^{\prime }$ , M<M'
• C. $\mu <{\mu }^{\prime }$ , M>M'
• D. $\mu >{\mu }^{\prime }$ , M>M'

Answer 1

The correct option is D

$\mu >{\mu }^{\prime }$ , M>M'

Let's draw the free body diagram of boy and box separately by the way if the boy pushes the box with a force F then by third law the box pushes the boy back with same force.

For the box to slide

F$\ge {\mu }^{\prime }{N}^{\prime }$

F$\ge {\mu }^{\prime }{M}^{\prime }g$ ..................(I)

Also given boy is not slipping

This means $\mu N\ge F$

$\mu Mg\ge F$ ......(II)

From (I) and (II)

$\mu Mg\ge {\mu }^{\prime }{M}^{\prime }g$

$\mu M\ge {\mu }^{\prime }{M}^{\prime }$

So option d can be true.