Question

In the pulley arrangement shown, the pulley $P_{2}$ is movable. Assuming 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)

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