Two balls have the same size and surface texture, but one is twice as heavy as the other. How many times larger is the terminal speed of the more massive ball falling through air than that of the lighter ball?
A) The balls fall with the same speed in air.
B) The massive ball's terminal speed is [2] $]^{1 / 2}$ times larger than the other's.
C) The massive ball's terminal speed is 2 times larger than the other's.
D) The massive ball's terminal speed is 4 times larger than the other's.
E) The massive ball's terminal speed is some other multiple of the other's (specify).

Question

Quizplus · Accepted Answer

The terminal speed $v_t$ is proportional to the square root of the mass ($m$) when other factors like size and drag coefficient are constant. Therefore, if one ball is twice as heavy, its terminal speed will be $\sqrt{2}$ times larger.

Two Balls Have the Same Size and Surface Texture, but One