Question

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

• A. $\mu(m+M) g$
• B. $\frac{\mu(m+M) g}{\mu+1}$
• C. $\frac{\mu(m+M) g}{\mu-1}$
• D. None of the above

Answer 1

Answer: (B)

As is clear from figure,
$R+T=(m+M) g$
The system will not move till
$T \leq F $ or $(T \leq \mu R)$
$T \leq \mu[(m+M) g=T]$
$T \leq \frac{\mu(m+M) g}{\mu+1}$
$ \therefore F_{\max }=\frac{\mu(m+M) g}{\mu+1}$