Question

Coefficient of friction between $A$ and $B$ is $\mu$. The minimum force $F$ with which $A$ will be pushed such that $B$ will not slip down is :

• A. $\frac{Mg}{\mu }$
• B. $\frac{mg}{\mu }$
• C. $\frac{(M+m)g}{\mu }$
• D. $\frac{(M-m)g}{\mu }$

Answer 1

The correct option is C $\frac{(M+m)g}{\mu }$

$F=(M+m)a\to \left(i\right)$

$N=ma\to \left(ii\right)$

$f=mg=\mu N\to \left(iii\right)$

$mg=\mu ma$

$a=g/\mu$

from eq (i)

$\frac{F}{M+m}=g/\mu$

$F=(M+m)g/\mu$

Option (C) is correct.