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A man of mass 60 kg is pulling a mass M by an inextensible light rope passing through a smooth and massless pulley as shown in figure. The coefficient of friction between the man and the ground is $μ = \frac{1}{2}$ . The maximum value of M that can be pulled by the man without slipping on the ground is approximately

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51 kg

26 kg

46 kg

32 kg

answer is D.

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Detailed Solution

$\begin{array}{l} T = Mg (T = tension in the rope) \\ N = 60 g - Tsin 60^{\circ} \end{array}$

(N = normal reaction between the man and the ground)

and $Tcos 60^{\circ} = μN$

Solving these three equations with proper substitutions we get

$M = 32 .15 kg \approx 32 kg$

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