Two bodies of masses \( m \) and \( 4 m \) are attached to a light string as shown in figure. A ...

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Two bodies of masses \( m \) and \( 4 m \) are attached to a light string as shown in 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)
(1) \( \frac{1}{4} \)
(2) \( \frac{3}{4} \)
(3) \( \frac{1}{2} \)
(4) \( \frac{1}{8} \)
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