First slide

Vertical circular motion

Question

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

Moderate

A

$\frac{1}{4}$
B

$\frac{3}{4}$
C

$\frac{1}{2}$
D

$\frac{1}{8}$

Solution

Velocity at lowest position = $\sqrt{2 g l (1 - \cos 60^{o})} = \sqrt{g l}$
$T = m g + \frac{m V^{2}}{l} = m g + \frac{m}{l} g l = 2 m g$ , $T = μ 4 m g$ $\Rightarrow$ $μ = \frac{1}{2}$

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