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Two bodies of mass m and 4m are attached to a spring as shown in the figure. The body of mass m hanging from a string of length l is executing periodic motion with amplitude $θ$ = 60° while other body is at rest on the surface. The minimum coefficient of friction between the mass 4m and the horizontal surface must be

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$\frac{2}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{3}$

answer is C.

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Detailed Solution

$h = l (1 - c o s 60^{\circ}) = \frac{l}{2}, v^{2} = 2 g h = g l N o w, T_{m a x} - m g = \frac{m v^{2}}{l} (a t b o t t o m m o s t p o i n t) ∴ T_{m a x} = 2 m g = μ_{s} (4 m g) ∴ μ_{s} = 0.5$

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