Question

In the pulley arrangement shown in the figure, the pulley $P_{2}$ is movable. Assuming the coefficient of friction between $m$ and surface to be $\mu$, the minimum 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

Answer: (A)

$f=2 T$ ...(i)
and $T=M g$ ...(ii)
If $m$ be at rest friction will be static
$f \leq \mu N$
$2 M g \leq \mu m g$
$\Rightarrow M=\frac{\mu m}{2}$