Question

A block of unknown mass is at rest on a rough horizontal surface. A force $F$ is applied to the block. The graph in the figure shows the acceleration of the block w.r.t the applied force.
The mass of the block and coefficient of friction are $(g=10{\text{m/s}}^2)$

• A. $2\text{kg},0.1$
• B. $2\text{kg},0.2$
• C. $1\text{kg},0.1$
• D. can't be determined

Answer 1

The correct option is B $2\text{kg},0.2$

We know that
$F_{net}=ma$ and $F_{net}=F-f$ where $f=$ Frictional force

$ma=F-f$
$ma=F-\mu mg$
$a=\frac{F}{m}-\mu g$
If $F=0,a=-2$ from graph
So, $-\mu g=-2$
$\mu =0.2$

If $a=0,F=4$
$\Rightarrow 0=\frac{4}{m}-0.2\left(g\right)$ $[g=10{\text{m/s}}^2]$
$\Rightarrow m=2\text{kg}$