Questions: Suppose that F = G M1 M2 / r^2. What is the value of F given that G=6.67 x 10^-11, M1=12 x 10^4, M2=7 x 10^4, and r=5 x 10^-3 ? Please round your answer to the nearest whole number (integer) and put it in the answer box.

Suppose that F = G M1 M2 / r^2. What is the value of F given that G=6.67 x 10^-11, M1=12 x 10^4, M2=7 x 10^4, and r=5 x 10^-3 ? Please round your answer to the nearest whole number (integer) and put it in the answer box.

Transcript text: Suppose that $F=\frac{G M_{1} M_{2}}{r^{2}}$. What is the value of $F$ given that $G=6.67 \times 10^{-11}, M_{1}=12$ $\times 10^{4}, M_{2}=7 \times 10^{4}$, and $r=5 \times 10^{-3}$ ? Please round your answer to the nearest whole number (integer) and put it in the answer box.

Solution

Solution Steps

Step 1: Identify the given values

Given:

$ G = 6.67 \times 10^{-11} $
$ M_1 = 12 \times 10^{4} $
$ M_2 = 7 \times 10^{4} $
$ r = 5 \times 10^{-3} $

Step 2: Substitute the values into the formula

Substitute the given values into the formula $ F = \frac{G M_1 M_2}{r^2} $: \[ F = \frac{(6.67 \times 10^{-11}) (12 \times 10^{4}) (7 \times 10^{4})}{(5 \times 10^{-3})^2} \]

Step 3: Simplify the expression

First, calculate the denominator: \[ (5 \times 10^{-3})^2 = 25 \times 10^{-6} \]

Next, calculate the numerator: \[ (6.67 \times 10^{-11}) (12 \times 10^{4}) (7 \times 10^{4}) = 6.67 \times 12 \times 7 \times 10^{-11 + 4 + 4} = 5602.8 \times 10^{-3} \]

Step 4: Divide the numerator by the denominator

\[ F = \frac{5602.8 \times 10^{-3}}{25 \times 10^{-6}} = \frac{5602.8}{25} \times 10^{3} = 224.112 \times 10^{3} \]

Step 5: Round to the nearest whole number

\[ F \approx 224112 \]

Step 6: Final answer

The value of $ F $ is approximately 224112.