Question

Keeping the angle of banking same, if the radius of curvature is made four times, the percentage increase in the maximum speed with which a vehicle can travel on a circular road is

• A. $25$%
• B. $50$ %
• C. $75$ %
• D. $100$ %

Answer 1

The correct option is D $100$ %

Angle of banking $\theta$ is given by relation,
$\tan \theta =\frac{v^2}{Rg}$
As angle of banking is same,
$\tan \theta =\frac{v_1^2}{Rg}=\frac{v_2^2}{4Rg}\Rightarrow v_2=2v_1$

% increase $=\frac{v_2-v_1}{v_1}\times 100=\frac{2v_1-v_1}{v_1}\times 100=100$


$\Rightarrow$ % increase$=100$%