A van is moving with a speed of $108 \mathrm{~km} / \mathrm{hr}$ on a level road where the coefficient of…
A van is moving with a speed of $108 \mathrm{~km} / \mathrm{hr}$ on a level road where the coefficient of friction between the tyres and the road is 0.5 . For the safe driving of the van, the minimum radius of curvature of the road shall be
(Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$ )
$40 \mathrm{~m}$
$180 \mathrm{~m}$
$120 \mathrm{~m}$
$80 \mathrm{~m}$
Solution
The correct option is (B).
Concept: For safe driving, the centripetal force must be less than limiting friction otherwise the vehicle will skid away from the road.
Mathematically it can be written as
$\frac{\mathrm{mv}}{\mathrm{r}} \leq \mu \mathrm{mg}$
where $m$ is the mass, $v$ is the velocity, $\mu$ is the coefficient of friction and $g$ is the acceleration due to gravity.
On plugging the values given in the question,
$r_{\min }=\frac{v^2}{\mu g}=\frac{30^2}{0.5 \times 10}=180 \mathrm{~m}$