Question

A boy of mass $4\text{kg}$ is standing on a piece of wood having mass $5\text{kg}$. If the coefficient of friction between the wood and the floor is $0.5$, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ______$\text{N}$.

$($Round off to the nearest integer$)$
$(g=10{\text{ms}}^{-2})$

Answer 1

FBD of the given situation is shown in the figure.

From equilibrium,
$f=T$
$\Rightarrow \mu R=T$
$\Rightarrow \mu \left[\right(M+m)g-T]=T$
$\Rightarrow 0.5\left[\right(4+5)10-T]=T$
$\Rightarrow 45-0.5T=T$
$\Rightarrow T=30\text{N}=F$