The roadway bridge over a stream is in the form of an are of a circle of radius r. A car is crossing the bridge with a speed v. Prove that the limiting speed of the car with which it can cross the bridge without leaving the ground at the highest point of the bridge is v`le sqrt(gr).`

Explanation

Let the mass of the car be m and speed of the car be b.
`therefore` Weight of the car = mg and centrifugal force = `(mv^(2))/(r )`.
At the highest point on the bridge, the car will not jump up from the road if the weight of the car `ge` centrifugal force.
`therefore" " mg ge (mv^(2))/(r ) " " or, " " gr ge v^(2)` .
or, ` v^(2) le " " gr " " or, " " v le sqrt(gr)`.