Question

A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tyre and the road is 2.0, find the maximum speed the car can take without skidding.

• A. 20 m/s
• B. 30 m/s
• C. 10 m/s
• D. 40 m/s

Answer 1

The correct option is B

30 m/s

Let the mass of the car be M. The forces on the car are
(a) weight Mg downward
(b) normal force N by the road upward
(c) friction $f_s$ by the road towards the centre
The car is going on a horizontal circle of radius R, so it is accelerating. The acceleration is towards the centre and its magnitude is $\frac{v^2}{R}$, where v is the speed. For vertical direction, acceleration = 0. Resolving the forces in vertical and horizontal directions and applying Newton's laws, we have
N = mg
and $f_s$ = $\frac{M{v}^2}{R}$.
As we are looking for the maximum speed for no skidding, it is a case of limiting friction and hence
$f_s$ = ${\mu }_s$ N = ${\mu }^s$ Mg.
So, we have
${\mu }_s$ Mg = $\frac{M{v}^2}{R}$
or, $v^2$ = ${\mu }_s$gR.
Putting the values, $v=\sqrt{2\times 10m/s^2\times 45m}$
= 30 m/s