A car is moving with a constant speed v on a flat circular track of radius R . The centripetal force required to keep the car in the circular path is F . If the car's speed is tripled and it moves on a new circular track of radius 3R , what will be the new required centripetal force?

Step-by-step solution

The centripetal force required for a car of mass m moving with speed v on a circular track of radius R is given by F = mv^2 R When the speed is tripled ( v' = 3v ) and the radius is tripled ( R' = 3R ), the new centripetal force F' is F' = m(v')^2 R' F' = m(3v)^2 3R F' = 9mv^2 3R F' = 3 ( mv^2 R ) F' = 3F Answer: 3F