Question

keeping the banking angle of the road as 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 20m to-

Answer 1

Answer: 24.2 m

Explanation:

On the curved road,

$F_{net}=F_{cen}$

$mgtan\theta =\frac{mv^2}{r}$

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

$\Rightarrow tan \theta= \frac{v^2}{rg}$

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

The radius of curvature is $r_1=20 m$

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

$\Rightarrow \frac{v_1^2}{r_1}=\frac{v_2^2}{r_2}\\ \Rightarrow r_2=\frac{(1.1 v_1)^2\times 20 m}{v_1^2}\Rightarrow r_2=24.2 m$

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