Question

A circular road of radius $1000\text{m}$ has a banking angle of ${45}^{\circ }$. The maximum safe speed (in $\text{m/s}$) of a car having a mass $2000\text{kg}$ will be (if the coefficient of friction between the tyres and the road is $0.3$) (Take $g=10{\text{m/s}}^2$)

• A. $136$
• B. $124$
• C. $99$
• D. $86$

Answer 1

The correct option is A $136$

Since, this is a case of banking of road with friction
$\therefore$ Maximum safe speed of the car for no skidding is given by
$v_{max}=\sqrt{\frac{Rg(\tan \theta +\mu )}{1-\mu \tan \theta }}$
Given, $\theta ={45}^{\circ },R=1000\text{m},\mu =0.3,g=10{\text{m/s}}^2$
$\therefore V_{max}=\sqrt{\frac{1000\times 10(\tan {45}^{\circ }+0.3)}{1-0.3\times \tan {45}^{\circ }}}$
$=\sqrt{\frac{10000\times 1.3}{0.7}}\approx 136\text{m/s}$