In the pulley arrangement shown in the figure, the pulley P2 is movable. Assuming the coefficient of friction between m and surface to be μ, the minimum value of M for which m is at rest is

Question

In the pulley arrangement shown in the figure, the pulley P2 is movable. Assuming the coefficient of friction between m and surface to be μ, the minimum value of M for which m is at rest is (A) M=(μ m/2) (B) m=(μ M/2) (C) M=(m/2 μ) (D) m=(M/2 μ)

Tardigrade Admin · Accepted Answer

f=2 T ...(i) and T=M g ...(ii) If m be at rest friction will be static f ≤ μ N 2 M g ≤ μ m g ⇒ M=(μ m/2)

Q. 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 $μ$ , the minimum value of $M$ for which $m$ is at rest is

$M = \frac{μ m}{2}$

$m = \frac{μ M}{2}$

$M = \frac{m}{2 μ}$

$m = \frac{M}{2 μ}$

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

Q. In the pulley arrangement shown in the figure, the pulley P2​ is movable. Assuming the coefficient of friction between m and surface to be μ, the minimum value of M for which m is at rest is

M=2μm​

m=2μM​