Question

Two bodies of masses m and 4 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 4m and the horizontal surface is (here pulley is light and smooth) is $\frac{1}{k}$, then k=___

Answer 1

Velocity at lowest position $=\sqrt{2gl(1-cos{60}^{\circ })}=\sqrt{gl}$
$T=mg+\frac{m{v}^2}{l}=mg+\frac{m}{l}gl=2mg$
$=\mu 4mg$
$\therefore \mu =\frac{1}{2}$