Question

question 2 of 25
two men each have a mass of 90 kg. if the gravitational force between them is 8.64×10^(-8) n, how far apart are they? g = 6.67×10^(-11) n·(m/kg)^2

a. 4.0 m
b. 3.2 m
c. 2.5 m
d. 5.0 m

Explanation:

Step1: Write the gravitational - force formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. Here, $m_1=m_2 = 90\ kg$, $F=8.64\times 10^{-8}\ N$, and $G = 6.67\times 10^{-11}\ N\cdot(m/kg)^2$.

Step2: Rearrange the formula to solve for $r$

Starting from $F = G\frac{m_1m_2}{r^2}$, we can cross - multiply to get $F\times r^2=G\times m_1\times m_2$. Then $r^2=\frac{G\times m_1\times m_2}{F}$. Substitute the given values: $r^2=\frac{6.67\times 10^{-11}\times90\times90}{8.64\times 10^{-8}}$.

Step3: Calculate the value of $r^2$

First, calculate the numerator: $6.67\times 10^{-11}\times90\times90=6.67\times 10^{-11}\times8100 = 5.4027\times 10^{-7}$. Then, $r^2=\frac{5.4027\times 10^{-7}}{8.64\times 10^{-8}}=\frac{5.4027}{8.64}\times10\approx0.625\times10 = 6.25$.

Step4: Calculate the value of $r$

Take the square root of $r^2$: $r=\sqrt{6.25}=2.5\ m$.

Answer:

C. 2.5 m