Question

A road bridge is in the form of a circular arc of radius $18m$. What is the limiting speed with which a car can traverse the bridge without losing contact at the highest point if the centre of gravity of the car is $0.4m$ above the ground? (in $m/s$)

• A. $12.36$
• B. $13.365$
• C. $17.36$
• D. $13.428$

Answer 1

The correct option is D $13.428$

The car will lose contact with bridge if centrifugal force exceeds weight of car.

so for maximum safe speed,

$m{v}^2/r=mg$

$v=\sqrt{rg}$

Here, r is distance from center of curvature to center of gravity of car. So, r = 18.4m

$v=\sqrt{18.4\ast 9.8}=13.428m/s$