Question

A vehicle of mass $m$ is driven along an un-banked curved path of radius of curvature $r$ with a speed $v$. If $\mu$ is necessary minimum coefficient of friction between tyres of vehicle and road so that the vehicle does not skid, then:

• A. $\mu \propto \frac{1}{v^2}$
• B. $\mu \propto r$
• C. $\mu \propto v^2$
• D. $\mu \propto \frac{1}{r}$

Answer 1

Answer: (C), (D)

For not skidding, $\mu N=\frac{m{v}^2}{r}$
or, $\mu =\frac{v^2}{rg}$

So, $\mu \propto v^2$ when $r$ is constant

and $\mu \propto \frac{1}{r}$ when $v$ is constant.