Question

Keeping the angle of banking of the road constant, the maximum speed of the vehicles is to be increased by $10\%$ . The radius of curvature of the road will have to be changed from $20m$ to

• A. $22m$
• B. $40m$
• C. $24.2m$
• D. $14.4m$

Answer 1

Answer: (C)

The banking angle $\theta$ is given by,
$tan\theta =\frac{v^2}{rg}$ ; where $v$ is velocity, $r$ is radius and $g$ is acceleration due to gravity.
$rgtan\theta =v^2$
$\Rightarrow r\propto v^2$
Hence, the ratio of the radius will be,
$\Rightarrow \frac{r_2}{r_1}={\left(\frac{v_2}{v_1}\right)}^2$
$\Rightarrow \frac{r_2}{20}={\left(\frac{\left(v+\frac{v}{10}\right)}{v}\right)}^2$
$\Rightarrow r_2=24.2m$ .