Figure shows a cylinder mounted on an horizontal axle. A massless string is wound on it two and a half turn and connected to two masses m and 2m. If the system is in limiting equilibrium, find the coe

Question

Figure shows a cylinder mounted on an horizontal axle. A massless string is wound on it two and a half turn and connected to two masses m and 2m. If the system is in limiting equilibrium, find the coefficient of friction between the string and the pulley surface.

TestHub · Accepted Answer

Capstan (belt-friction) relation for limiting equilibrium: $T_{2} = T_{1} e^{μ θ}$ .

Here $T_{2} = 2 m g$ , $T_{1} = m g$ and the string is wound 2.5 turns: $θ = 2.5 \times 2 π = 5 π$ .

$2 = e^{5 π μ} \Rightarrow μ = \frac{l n 2}{5 π} = \frac{1}{5 π} ℓ n 2$ - (C)

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