The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 600 pounds 2,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth?
A)He will weigh 3,750 pounds.
B)He will weigh 1,500 pounds.
C)He will weigh 480 pounds.
D)He will weigh 96 pounds.
E)He will weigh 240 pounds.

Question

Quizplus · Accepted Answer

The weight of a body varies inversely with the square of the distance from the center of the Earth, so $F = k/d^2$, where $k$ is a constant. Given $F = 600$ pounds at $d = 2000$ miles, we can find $k = 600 \times 2000^2$. At $d = 5000$ miles, the weight $F = k/5000^2$. Substituting the value of $k$ from the first condition, $F = (600 \times 2000^2) / 5000^2 = 96$ pounds.

The Weight F of a Body Varies Inversely with the Square