Question

Two bodies of masses $m$ and $4\, m$ are attached to a light string as shown in the figure. A body of mass $m$ hanging from string is executing oscillations with angular amplitude $60^{\circ}$, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass $4 \,m$ and the horizontal surface is (here pulley is light and smooth)

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

Answer: (C)

Velocity at lowest position,
$v=\sqrt{2 g l\left(1-\cos 60^{\circ}\right.}=\sqrt{g l}$
$ T=m g+\frac{m v^{2}}{l}=m g+\frac{m}{l} g l=2 m g$
$\therefore T =\mu 4 m g$
$\Rightarrow \mu=\frac{1}{2}$