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
$T\le F$ or $(T\le \mu R)$
$T\le \mu [(m+M)g=T]$
$T\le \frac{\mu (m+M)g}{\mu +1}$
$\therefore F_{\max }=\frac{\mu (m+M)g}{\mu +1}$