Question

A person is driving a vehicle at uniform speed of $5{ms}^{-1}$ on a level curved track of radius 5 m. The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take g = $10{ms}^{-2}$.
Choose the correct statement.

• A. A person will slip if $v^2=5{ms}^{-1}$
• B. A person will slip if $v^2>5{ms}^{-1}$
• C. A person will slip if $v^2<5{ms}^{-1}$
• D. A person will slip if $v^2>10{ms}^{-1}$

Answer 1

Answer: (B)

A person will slip if $v^2>5{ms}^{-1}$

Person will slip if centripetal force $\frac{m{v}^2}{r}$ is greater than frictional force $\mu mg$ where $m$ is mass off vehicle, $v$ is velocity, $r$ is radius ($5m$) and $\mu$ is coefficient of static friction ($0.1$), $g$ is acceleration due to gravity ($m/s^2$).

Therefore condition of slipping

$\frac{m{v}^2}{r}>\mu mg$

i.e. $v^2>\mu rg$

i.e. $v^2>5$