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

Answer 1

The correct option is D $200m$

FORMULA USED: $v=\sqrt{rg\tan \theta }$

Given: $v_2=2v_1,r_1=50m$
$v=\sqrt{rg\tan \theta }$ or$\frac{\tan \theta }{g}=\frac{v^2}{r}$
As angle is kept same and speed is doubled
So, we can say
$\frac{\tan \theta }{g}=$constant$=\frac{v^2}{r}$

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

$\frac{v_1^2}{r_1}=\frac{4v_1^2}{r_2}$​​​​​​

$r_{2=4r_1}=4\left(50\right)=200m$