Question

A circular road of radius $1000m$ has banking angle ${45}^o$. The maximum safe speed of a car having mass $2000kg$ will be, if coefficient of friction between tyre and road is $0.5$:

• A. $172m/s$
• B. $124m/s$
• C. $99m/s$
• D. $86m/s$

Answer 1

The correct option is A $172m/s$

Given that: $r=1000m,\theta ={45}^0,\mu =0.5,m=2000kg$

We know that maximum safe velocity for a banked is given by :

$v=\sqrt{\frac{rg(\tan \theta +\mu )}{1-\mu tan\theta }}$

hence on putting the given values, we get

$v=\sqrt{\frac{1000\times 9.8\times (\tan 45+0.5)}{1-0.5\tan 45}}$

or $v=172m/s$

hence option A is correct