Question

A car travels at a constant speed of $30\text{m/s}$ around a level circular bend of radius $100\text{m}$. What is the minimum coefficient of static friction between the tires and the road in order for the car to go round the bend without skidding?

• A. $0.8$
• B. $0.9$
• C. $0.7$
• D. $0.55$

Answer 1

The correct option is B $0.9$

Frictional force will be the only source of necessary centripetal force.
For finding minimum ${\mu }_s$, friction should be acting at its limiting value
$\therefore f_{max}={{\mu }_s}_{min}mg$.............($1$)

Equation of dynamics
$f_{max}=\frac{m{v}^2}{r}={{\mu }_s}_{min}mg$............($2$)


$\therefore {{\mu }_s}_{min}=\frac{v^2}{gr}=\frac{{30}^2}{10\times 100}=\frac{900}{1000}$
or ${{\mu }_s}_{min}=0.9$