A mountain road has a curve of radius 40 m. If at the curve the road is 4m wide and its outer edge is 0.80 m higher than the inner edge. find the maximum speed for which the curve is intended.

The radius of curvature of a railway track at a bend is 500 m. The distance between the two tracks is 1 m and the outer line is 4 cm higher than the inner. At what maximum speed can a train bend round the curve without exerting lateral pressure on the outer line?

A car passes over a convex bridge. The centre of gravity of the car follows an arc of a circle of radius 30 m. Assuming that the car has a mass of 1000 kg, find the force that the car will exert at the highest point on the bridge, if the velocity of the car is 15 m cdot s^(-1) . At what speed will the car lose contact with the road?

A circular race track of radiu 400 m is banked at an angle of 10^(@) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the (i) optimum speed of the race car to avoid wear and tear on its tyres? maximum permissible speed to avoid slipping?