Question

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

• A. 16m
• B. 18m
• C. 24.20 m
• D. 30.5 m

Answer 1

Answer: (C)

24.20 m

On the curved road,

$F_{net}=F_{cen}$

$mgtan\theta =\frac{m{v}^2}{r}$

where m is the mass, v is the speed, is the banking angle and r is the radius of the curvature.

$⟹tan\theta =\frac{v^2}{rg}$

It is the given that banking angle would be kept same. we want to increase the speed by 10%. It means new speed, $v_2=1.1v_1$

The radius of curvature is $r_1=20m$

we want to find the new radius of curvature, $r_2$

$⟹\frac{{v_1}^2}{r_1}=\frac{{v_2}^2}{r_2}$

on solving above equation with given values we get

$r_2=24.2m$

The radius of curvature of the road will have to be changed from 20m to-24.2 m.