A boy of mass M is applying a horizontal force P to slide a box of mass M' on a rough horizontal surface. 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?

Horizontal force (P) applied by the shoes of the boy on the ground must be equal to the horizontal force applied by the boy on the box.Shoes of the boy must not slide on the surface.Therefore µmg>P.Also the box will slide if P > µ'mg..: µmg > µ'm'g ⇒ µm > µ'm'So if  µ < µ' and m < M' The product µm will be less than the product µm'.