Question

A $1200\text{kg}$ automobile rounds a level curve of radius $200\text{m}$, on an unbanked road with a velocity of $72\text{km/h}$. What is the minimum coefficient of static friction between the tyres and road in order that the automobile may not skid? $(g=10{\text{m/s}}^2)$

• A. $0.15$
• B. $0.2$
• C. $0.3$
• D. $0.4$

Answer 1

The correct option is B $0.2$

Frictional force is the only source of centripetal force.
i.e $f=\frac{m{v}^2}{r}$
But we know that $f\le f_{max}={\mu }_{s}N$
$\therefore \frac{m{v}^2}{r}\le {\mu }_{s}N$........($1$)

For vertical equilibrium of car;
$N=mg$.......($2$)

Combining Eq.($1$) and ($2$):
$\frac{m{v}^2}{r}\le {\mu }_{s}mg$
$\Rightarrow {\mu }_s\ge \frac{v^2}{gr}$
Here, $v=72\text{km/hr}=72\times \frac{5}{18}=20\text{m/s},r=200\text{m}$

$\therefore {\mu }_{smin}=\frac{{20}^2}{10\times 200}=0.2$