Question

A circular smooth road of radius $r=20m$ is banked for vehicles moving at a speed of $v=36kmph$. If the friction coefficient between the road and the road and the Tyre is $0.3$, find the maximum speed of a vehicle going around this curved road.

• A. $29.39kmph$
• B. $39.29kmph$
• C. $40.39kmph$
• D. None of these

Answer 1

The correct option is C $40.39kmph$

$v=36km/hr=10m/secForsmoothroadtan\theta =\frac{v^2}{rg}=\frac{10\left(10\right)}{10\left(20\right)}=\frac{1}{2}\omega =0.3tan\theta =\frac{v^2-\omega rg}{rg+\omega v^2}200+0.3v^2=2v^2-60v^2=152.9v=44.4km/hr$