Question

A road of width $20\text{m}$ forms an arc of radius $15\text{m}$, its outer edge is $2\text{m}$ higher than its inner edge. For what speed the road is banked?

• A. $\sqrt{10}\text{m/s}$
• B. $\sqrt{14.7}\text{m/s}$
• C. $\sqrt{9.8}\text{m/s}$
• D. None of these

Answer 1

The correct option is B $\sqrt{14.7}\text{m/s}$


Given $R=15\text{m}$
Let $V$ be optimum velocity of car
We know that
$V^2=gR\tan \theta$
From triangle, $\tan \theta =\frac{2}{\sqrt{396}}$
$V^2=10\times 15\times \frac{2}{\sqrt{396}}=\frac{300}{\sqrt{396}}$
$V=\sqrt{14.7}\text{m/s}$