Question

A car moves on a horizontal track of radius $r$, the speed increasing constantly at rate $\frac{dv}{dt}$$=a$. The coefficient of friction between road and tyre is $\mu$. Find the speed at which the car will skid.

• A. ${\left[({\mu }^2{g}^2+a^2)r^2\right]}^{1/4}$
• B. $\sqrt{\mu gr}$
• C. ${\left[({\mu }^2{g}^2-a^2)r^2\right]}^{1/4}$
• D. $\sqrt{ar}$

Answer 1

Answer: (C)

${\left[({\mu }^2{g}^2-a^2)r^2\right]}^{1/4}$

For skidding: $\sqrt{a^2+{\left(\frac{v^2}{r}\right)}^2}\ge \mu g$

or ${\left(\frac{v^2}{r}\right)}^2={\mu }^2{g}^2-a^2$, for the least speed at which the car will skid.

or, $v={\left[({\mu }^2{g}^2-a^2)r^2\right]}^{1/4}$.