A man whose mass is 80 kg on the earth's surface is in a spacecraft at a height of 2 earth radii above the earth's surface. His weight there is
A) 87 N.
B) 196 N.
C) 261 N.
D) 784 N.

Question

Quizplus · Accepted Answer

The weight of an object is given by the formula $W = \frac{G M m}{r^2}$, where $W$ is the weight, $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the object, and $r$ is the distance from the center of the Earth. At a height of 2 Earth radii above the Earth's surface, the distance $r$ is 3 Earth radii. Since the weight is inversely proportional to the square of the distance from the center of the Earth, if the distance triples (from 1 Earth radius to 3 Earth radii), the weight decreases by a factor of $3^2 = 9$. On the Earth's surface, the man's weight is $80 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 784 \, \text{N}$. At 2 Earth radii above the surface, his weight is $784 \, \text{N} / 9 = 87 \, \text{N}$.

A Man Whose Mass Is 80 Kg on the Earth's