Question

Statement - I :

Two blocks of masses m and M are placed on a horizontal surface. The coefficient of friction between two blocks is ${\mu }_1$ and that between the block M and horizontal surface is ${\mu }_2$. The maximum force that can be applied to block M so that the two blocks move without slipping is $F=({\mu }_1+{\mu }_2)(M+m)g$

Statement - II:

F$=$Total maximum acceleration

• A. Statement1 is True, Statement2 is True; Statement2 is a correct explanation for Statement1
• B. Statement1 is True, Statement2 is True; Statement2 is NOT a correct explanation for Statement1
• C. Statement1 is True, Statement2 is False
• D. Statement1 is False, Statement2 is True

Answer 1

The correct option is C Statement1 is True, Statement2 is False

Friction between m and $M,f={\mu }_{1}mg$ and between M and surface, $f^{\prime }=$${\mu }_2(M+m)g$
$\therefore$ For system to have acceleration a net force
$F=(M+m)a+{\mu }_2(M+m)g$

Acceleration of $massm,a=\frac{{\mu }_{1}mg}{m}={\mu }_{1}g$
$\therefore F={\mu }_1(M+m)g+{\mu }_2(M+m)g$
$=({\mu }_1+{\mu }_2)(M+m)g$