Question

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20%, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]}

• A. 28.8 m
• B. 14.4 m
• C. 8.8 m
• D. 4.8 m

Hint:

For constant banking, the radius must be increased by the square of the speed factor ($1.2^2 = 1.44$).

Answer 1

The Correct Option is C

Step 1: Formula
Maximum safe speed $v = \sqrt{rg \left( \frac{\mu + \tan \theta}{1 - \mu \tan \theta} \right)}$.
Since $\mu, \theta$ are constant, $v \propto \sqrt{r} \implies v^2 \propto r$.
Step 2: Proportionality
$\frac{r_2}{r_1} = \left( \frac{v_2}{v_1} \right)^2$.
Given $v_2 = 1.2 v_1$, so $r_2 = r_1 \times (1.2)^2 = 20 \times 1.44 = 28.8 \text{ m}$.
Step 3: Increase in Radius
Increase $= r_2 - r_1 = 28.8 - 20 = 8.8 \text{ m}$.
Final Answer: (C)