Question

A curved road of radius $50m$ is banked at 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. $25\text{m}$
• B. $100\text{m}$
• C. $150\text{m}$
• D. $200\text{m}$

Answer 1

The correct option is D $200\text{m}$


By the free body diagram and writing the force equation we get,

$N\cos \theta =mg...\left(i\right)$
$N\sin \theta =\frac{m{v}^2}{r}...\left(ii\right)$
Now by dividing both the above equations, we get,

$\theta ={\tan }^{-1}\left(\frac{v^2}{rg}\right)$
Condition for banked road is,
$\tan \theta =\frac{v^2}{rg}$, therefore, when speed $v$ is doubled and $\theta$ remains the same we have
$\frac{\frac{(2v{)}^2}{r^{{}^{\prime }}g}}{\frac{v^2}{rg}}=1\Rightarrow r^{\prime }=4r$
$\therefore$ New radius of curvature should be
$r^{\prime }=4r=4\times 50=200\text{m}$