Prove that a motor car moving over a
(i) Convex bridge is lighter than the same car resting on the same bridge.
(ii) Concave bridge is heavier than the same car resting on the same bridge.

Explanation

Apparent weight of car = N (normal reaction)
(i) Convex bridge
The motion of the motor car over a convex bridge is the motion along the segment of a circle. The centripetal force is provided by the difference of weight mg of the car and the normal reaction N of the bridge.
`therefore " mg " - N = (mv^(2))/(r )`
or N = mg - `(mv^(2))/(r )`
Clearly N `lt` mg, i.e., the apparent weight of the moving car is less than the weight of the stationary car.
(ii) Concave bridge N – mg = `(mv^(2))/(r )`
Apparent weight N = mg + `(mv^(2))/(r )`