Question

Radius of the curved road on national highway is $R$. Width of the road is $b$. The outer edge of the road is raised by $h$ with respect to inner edge so that a car with velocity $v$ can pass safely over it. The value of $h$ is

• A. $\frac{v^{2}b}{Rg}$
• B. $\frac{v}{Rgb}$
• C. $\frac{v^{2}R}{bg}$
• D. $\frac{v^{2}b}{R}$

Answer 1

The correct option is A $\frac{v^{2}b}{Rg}$

In equilibrium , $N\sin \theta =\frac{m{v}^2}{R}$ (centripetal force) and $N\cos \theta =mg$

Thus, $\tan \theta =\frac{v^2}{Rg}$

or $\frac{h}{b}=\frac{v^2}{Rg}$

or $h=\frac{v^{2}b}{Rg}$