A man of mass M is standing on a board of mass m. The friction coefficient between the board and the floor is $μ,$ shown in figure. The maximum force that the man can exert on the rope so that the board does not move is

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None of the above

$\frac{μ (m + M) g}{μ - 1}$

$μ (m + M) g$

$\frac{μ (m + M) g}{μ + 1}$

answer is B.

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Detailed Solution

As is clear from figure,

$R + T = (m + M) g$

$R = (m + M g) - T$

The system will not move till

$T \leq F o r (T \leq μ R)$

$T \leq μ [(m + M) g = T]$

$T \leq \frac{m (m + M) g}{μ + 1} ∴ F_{\max} = \frac{μ (m + M) g}{μ + 1}$

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