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 $20m$. to

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

Answer 1

Answer: (C)

$24.20m$

Given : $r=20$ m

Let the safe speed initially be $v$ and $\theta$ be the banking angle.

$\therefore$ $v=\sqrt{grtan\theta }$ where $r=20$ m

Now new safe speed $v^{\prime }=1.1v$

$\therefore$ $v^{\prime }=\sqrt{g{r}^{\prime }tan\theta }=1.1v$

OR $1.1\times \sqrt{grtan\theta }=\sqrt{g{r}^{\prime }tan\theta }$

OR $r^{\prime }=(1.1{)}^{2}r$

$⟹$ $r^{\prime }=1.21\times 20=24.20$ m