Question

A car moves at a constant speed on a straight but hilly road. One section has a crest and dip of the same $250m$ radius. What is the greatest speed at which the car can move without leaving the road at the top of the hill?

• A. $5m{s}^{-1}$
• B. $25m{s}^{-1}$
• C. $30m{s}^{-1}$
• D. $50m{s}^{-1}$

Answer 1

The correct option is D $50m{s}^{-1}$

Here,

$mg-N=\frac{m{v}^2}{R}$

$N=mg-\frac{m{v}^2}{R}$

When the car would be just to leave the road in that case Normal reaction can be consider as zero.

$0=mg-\frac{m{v}_{max}^2}{r}$

Therefore, $v_{max}=\sqrt{gR}$ =$\sqrt{10\ast 250}$ =50m/s