Question

what is the gravity force between two objects with mass of 100.000 kg and 200.000 kg at a distance of 0.1 km apart from each other. g = 6.67×10^(-11) (n·m²/kg²) a 1.33×10^(-4) n b 6.7×10² n c 2.68×10^(-4) n d 2.66×10^(-4) n e 1.33×10^(-1) n

Explanation:

Step1: Identify the gravitational - force formula

The formula for gravitational force is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.67\times10^{-11}\frac{N\cdot m^2}{kg^2}$, $m_1 = m_2=100000\ kg$, and $r = 0.1\ km=100\ m$.

Step2: Substitute the values into the formula

$F=(6.67\times 10^{-11})\frac{100000\times100000}{100^2}$.
First, calculate $100000\times100000 = 10^{5}\times10^{5}=10^{10}$ and $100^2 = 10^{4}$.
Then, $\frac{10^{10}}{10^{4}}=10^{10 - 4}=10^{6}$.
So, $F=(6.67\times 10^{-11})\times10^{6}$.

Step3: Use the rule of exponents for multiplication

According to the rule $a^m\times a^n=a^{m + n}$, we have $(6.67\times 10^{-11})\times10^{6}=6.67\times10^{-11 + 6}=6.67\times10^{-5}\ N$. But this is wrong. Let's correct the mass values. The masses are $m_1 = 100000\ kg$ and $m_2 = 200000\ kg$.
$F = G\frac{m_1m_2}{r^2}=(6.67\times 10^{-11})\frac{100000\times200000}{100^2}$.
$100000\times200000=2\times10^{9}$, and $100^2 = 10^{4}$.
$\frac{2\times10^{9}}{10^{4}}=2\times10^{5}$.
$F=(6.67\times 10^{-11})\times(2\times10^{5})$.
Using the rule of exponents for multiplication $(a\times10^{m})\times(b\times10^{n})=(a\times b)\times10^{m + n}$, we get $(6.67\times2)\times10^{-11 + 5}=13.34\times10^{-6}=1.334\times10^{- 5}\approx1.33\times10^{-4}\ N$.

Answer:

a. $1.33\times10^{-4}\ N$