Question

A curved road of 50 metres in radius is bank 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 to be changed to

Answer 1

We have the expression with the velocity of a body moving along a banked road.

$\tt{v^2=rg\tan (\theta+\phi)}$

where $\tt{r}$ the radius of the curve, $\tt{g}$ the acceleration due to gravity and$\tt{\theta}$ the angle of banking.

Here $\tt{\tan\phi}$ represents the coefficient of friction, i.e., $\tt{\mu=\tan\phi}.$

For the constant angle of banking with same friction, we get the relation,

$\tt{v^2\propto r}$

I.e., if velocity is doubled, then the radius of curve will be quadrupled.