Question

In the pulley arrangement shown in figure, pulley $P_2$ is movable. Assuming the coefficient of friction between the block having mass $m$ and the surface is $\mu$, find the maximum value of $M$ for which $m$ is at rest.

• A. $\mu m/2$
• B. $\mu m/3$
• C. $\mu m/6$
• D. $\mu m/4$

Answer 1

The correct option is A $\mu m/2$


From F.B.D of $M$
$T=Mg$
We know, for limiting case of friction force, $f=\mu mg$
and from F.B.D of $m$
$f=\mu mg\ge 2T$ so that $m$ will continue to be at rest.
Therefore $\mu mg\ge 2Mg$
$\Rightarrow \mu m\ge 2M$
So, maximum value of $M=\frac{\mu m}{2}$
Option (a) is correct.