A car of mass `m` moving over a concave bridge of radius `r` .Find the normal reaction acting on car when it is at lowest point the bridge

Explanation

The motion of the motor car over a concave bridge `AB` is the motion along the segment of a circle `AB` (Fig )

The centripetal force is provided by the difference of normal reacttion `R` of the bridge and weight `mg` of the car.
`:. R- mg = (mv^(2))/(r )`
or `R = mg + (mv^(2))/(r )`
Clearly `R lt mg ` i,e the weight of moving car is greater than the weight of the statinary car .