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)

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)

Infinity Learn · Accepted Answer

Velocity at lowest position $$=$$ $$2gl(1$$−$$cos60o)=glT=mg+mV2l=mg+mlgl=2mg$$, $$T=$$μ$$4mg$$⇒μ$$=12$$

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