Question

A vehicle is moving with a velocity $v$ on a curved road of width $b$ and radius of curvature $R$. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edge of the road is

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

Answer 1

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

We know that for the vehicle banking
on a curved path, $tan\theta =\frac{v^2}{rg}$.

Here, the vehicle moves with velocity
$v$ and radius of curvature $R$ and width is b.

So, here $\theta$ is small (refer figure) and thus, $sin\theta =\frac{h}{b}=tan\theta$.

Now, we can equate $\frac{h}{b}=\frac{v^2}{Rg}$
$\Rightarrow h=\frac{b{v}^2}{Rg}$, will be the required elevation between the outer and inner edges of the road.