Question

A curved road of $50m$ in radius is banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

• A. 200 m
• B. 100 m
• C. 50 m
• D. None of the above

Answer 1

The correct option is A 200 m

$\frac{v^2}{g}=\frac{\left(\tan \theta +{\mu }_s\right)}{\left(1-{\mu }_s\tan \theta \right)}$

$\frac{v^2\times \left(1-{\mu }_s\tan \theta \right)}{g\times \left(\tan \theta +{\mu }_s\right)}=r$

$\frac{r^{\prime }}{r}=\left(\frac{v_1^2}{v^2}\right)=\frac{2^2{v}^2}{v^2}$

$r^{\prime }=\left(r\times 2^2\right)$

$=50\times 4$

$r^{\prime }=200$