Question

In the pulley arrangement shown below, the pulley $P_2$ is movable. Assuming the coefficient of friction between m and surface to be $\mu$, the maximum value of M for which m is at rest is

• A. $M=\frac{\mu m}{2}$
• B. $m=\frac{\mu m}{2}$
• C. $M=\frac{m}{2\mu }$
• D. $m=\frac{M}{2\mu }$

Answer 1

The correct option is A

$M=\frac{\mu m}{2}$

$f=2T$ and $T=Mg$

If m be at rest friction will be static

$f\le \mu N$

$2Mg\le \mu mg\Rightarrow M=\frac{\mu m}{2}$