Question

A body is moving along a rough horizontal surface with an initial velocity $6m/s$. If the body comes to rest after travelling $9m$, then the coefficient of sliding firction will be

• A. $0.4$
• B. $0.2$
• C. $0.6$
• D. $0.8$

Answer 1

The correct option is B $0.2$

We know that frictional force is given by $F={\mu }_{s}N={\mu }_s\times mg$

where ${\mu }_s$ is the coefficient of sliding friction.

If $a$ is the deceleration of the body,
$ma={\mu }_s\times mg\Rightarrow {\mu }_s=\frac{a}{g}$

Now, by third equation of motion we know that

$v^2-u^2=2as$
$v=0$ (as body comes to rest)
$\Rightarrow a=-\frac{u^2}{2s}=-\frac{6^2}{2\times 9}=-2m/s^2$
($-ve$ sign shows that the body is retarding or slowing down)

$\therefore {\mu }_s=\frac{a}{g}=\frac{2}{10}=0.2$