At what distance from the center of the Earth would one's weight be one third of that recorded on the Earth's surface? Let the Earth's radius be $\mathrm{R}$.
A) $1.7 \mathrm{R}$
B) $0.4 \mathrm{R}$
C) $1.4 \mathrm{R}$
D) $0.5 \mathrm{R}$
E) 3R
F) $\mathrm{R}$

Question

Quizplus · Accepted Answer

EThe gravitational force (and thus weight) varies inversely with the square of the distance from the center of the Earth. If your weight is one third on the surface, then $ \frac{1}{3} = \left( \frac{R}{d} \right)^2 $, where $d$ is the distance from the center of the Earth where the weight is one third. Solving for $d$, we get $d = \sqrt{3}R$. The closest answers to $\sqrt{3}R$ are $1.7R$ and $3R$, but since $\sqrt{3}$ is approximately 1.732, the correct answer is $1.7R$ (A) and $3R$ (E) for the distance from the center of the Earth. However, upon reevaluation, the correct interpretation should solely be $1.7R$ (A) because the calculation directly leads to this value, and $3R$ (E) was mistakenly included due to a misinterpretation of the calculation process.

At What Distance from the Center of the Earth Would R\mathrm{R}R

At What Distance from the Center of the Earth Would $\mathrm{R}$