Question

1. an object weighs 200 newtons at a distance of 100 kilometers above the center of a small uniform planet. how much will the object weigh at 200 kilometers above the planets center?

a. 400 newtons
b. 100 newtons
c. 50.0 newtons
d. 25.0 newtons

Explanation:

Step1: Recall gravitational - force formula

The gravitational force $F$ is inversely proportional to the square of the distance $r$ from the center of the planet, i.e., $F = \frac{GMm}{r^{2}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, $m$ is the mass of the object. Let $F_1$ be the force at distance $r_1$ and $F_2$ be the force at distance $r_2$. Then $\frac{F_1}{F_2}=\frac{r_2^{2}}{r_1^{2}}$.

Step2: Identify given values

We know that $F_1 = 200$ N, $r_1=100$ km, and $r_2 = 200$ km.

Step3: Calculate the new force

Substitute the values into the ratio formula: $\frac{F_1}{F_2}=\frac{r_2^{2}}{r_1^{2}}$. So, $F_2=F_1\times\frac{r_1^{2}}{r_2^{2}}$. Plugging in the numbers: $F_2 = 200\times\frac{100^{2}}{200^{2}}=200\times\frac{10000}{40000}=50$ N.

Answer:

c. 50.0 newtons