A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static friction

Question

A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:

Accepted Answer

1. **Forces on a Level Road:** On a level circular road, the vertical forces (weight $mg$ and normal reaction $N$) balance each other, so $N = mg$. The necessary centripetal force required for the car to move in a circle of radius $R$ is provided solely by the static friction ($f_s$) between the tyres and the road.
2. **Centripetal Force Condition:** The centripetal force is given by $F_c = \frac{mv^2}{R}$. This force must be less than or equal to the maximum static friction ($f_{s,max}$) to prevent skidding.
   $$ \frac{mv^2}{R} \le f_{s,max} $$
   $$ f_{s,max} = \mu_s N = \mu_s mg $$
3. **Derivation:**
   $$ \frac{mv^2}{R} \le \mu_s mg $$
   $$ v^2 \le \mu_s Rg $$
   $$ v \le \sqrt{\mu_s Rg} $$
   Therefore, the maximum speed is $v_{max} = \sqrt{\mu_s Rg}$.
   (Reference: NCERT Class 11, Physics Part I, Chapter 5, Section 5.10, Eq. 4.18).

Step-by-Step Solution

Practice All PHYSICS Questions