Question

Assuming the coefficient of friction between the road and tires of a car to be 0.5, the maximum speed with which the car can move around a curve of $40.0m$ radius without slipping if the road is unbanked, should be

• A. $25m/s$
• B. $19m/s$
• C. $14m/s$
• D. $11m/s$

Answer 1

The correct option is C $14m/s$

Let v be the maximum speed of the car which is moving around a curve of radius 40 m and it is moving with this velocity without slipping. So, frictional force = centripetal force

$\mu mg=\frac{m{v}^2}{R}$

$v^2=\mu gR$

$v^2=0.5\times 40\times 9.8$

$v^2=196m/s$

$v=14m/s$

$\mu$ is coefficient of friction between car and tyre.

R is the radius of curve

v is the velocity of a car