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 $v^{2} < 5\, m^2s ^{-2}$
• D. A person will not slip if $v ^{2} > 5\, m^2 s ^{-2}$

Answer 1

Answer: (B)

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

Answer 2

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