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

Solution

## The correct option is C Statement1 is True, Statement2 is FalseFriction between m and $$M ,f=\mu_{1}mg$$ and between M and surface, $$f'=$$$$\mu_{2}(M+m)g$$$$\therefore$$ For system to have acceleration a net force$$F = (M + m) a + \mu_{2} (M + m) g$$Acceleration of $$\displaystyle \mathrm{mass \ m},a=\frac{\mu_{1}mg}{m}=\mu_{1}g$$$$\therefore F=\mu_{1}(M+m)g+\mu_{2}(M+m)g$$        $$=(\mu_{1}+\mu_{2})(M+m)g$$Physics

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