Question

The maximum speed with which a vehicle can negotiate a curved road, which is banked at the angle, $\theta ={\tan }^{-1}\left(0.24\right)$ is $54\text{km/hr}$. If another road is flat and the vehicle has to negotiate a curve with the same maximum speed, coefficient of friction between road and tyre should be
(Radius of both the road is same)

• A. $0.35$
• B. $0.5$
• C. $0.8$
• D. $0.24$

Answer 1

The correct option is D $0.24$

Given:
$v=54\text{km/hr}=54\times \frac{5}{18}\text{m/s}=15\text{m/s}$

For frictionless banked road, maximum safe speed is given by

$v=\sqrt{Rg\tan \theta }$

$v^2=Rg\tan \theta$

${15}^2=Rg\times 0.24........\left(1\right)$

And for the flat road with friction,

$v=\sqrt{\mu Rg}$

$v^2=\mu Rg$

${15}^2=\mu Rg.....\left(2\right)$

Equating equations $\left(1\right)\&\left(2\right)$, we get

$\mu =0.24$

Therefore, option $\left(C\right)$ is the correct answer.