Question

A car goes on a horizontal circular road of radius $R$, the speed increasing at a constant rate $\frac{dv}{dt}=a$. The friction coefficient between the road and the tyre is $\mu$. Find the maximum value of speed at which the car is safe to drive $.$

Answer 1

Turning on a level road:

$N=mg$

$f\ge \frac{m{V}^2}{R}$ (so that the vehicle may not slip)

$⟹\mu mg\ge \frac{m{V}^2}{R}$

$⟹V\le \sqrt{\mu Rg}$

$⟹V_{max}=\sqrt{\mu Rg}$