An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500 m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change

By Factor of 4

Explanation:

The expression for centripetal acceleration is given as,

a = v²/r ... equation 1

Where a = centripetal acceleration, v = speed, r = radius of the circle.

Case 1

Given: v = 150 m/s, r = 500 m

Substitute into equation 1

a = 150²/500

a = 22500/500

a = 45 m/s².

Case 2

Given: v = 300 m/s, r = 500 m

Also substitute into equation 1

a = 300²/500

a = 180 m/s²

Factor of change of the acceleration = 180/45

Factor of change of the acceleration = 4.

Hence the acceleration will change by a factor of 4