An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the speed remained the same, by what factor would its centripetal acceleration change?
A) 0.25
B) 0.50
C) 1.00
D) 2.00
E) 4.00

Question

Quizplus · Accepted Answer

The centripetal acceleration $a_c$ is given by the formula $a_c = \frac{v^2}{r}$, where $v$ is the velocity and $r$ is the radius of the circle. If the radius $r$ is doubled (from 500 m to 1000 m) while keeping the speed $v$ constant, the new acceleration is $\frac{1}{2}$ of the original acceleration, because the radius $r$ is in the denominator. Therefore, the factor by which the centripetal acceleration changes is 0.50.

An Airplane Flies in a Horizontal Circle of Radius 500