Question

What is the maximum speed with which a vehicle can negotiate a convex bridge of radius $10\text{m}$ without leaving the surface of the road.
(Take $g=10{\text{m/s}}^2$)

• A. $18\text{kmph}$
• B. $32\text{kmph}$
• C. $36\text{kmph}$
• D. $42\text{kmph}$

Answer 1

The correct option is C $36\text{kmph}$


Resolving the forces
$mg-N=\frac{m{v}^2}{r}$
For the vehicle to be in contact with the road,
$N\ge 0$
$⟹mg\ge \frac{m{v}^2}{r}$
$⟹v\le \sqrt{rg}$
$⟹v_{max}=\sqrt{rg}$
$⟹v_{max}=\sqrt{10\times 10}=10\text{m/s}$
$⟹v_{max}=36\text{kmph}$