Question

question 13 of 25
two asteroids with masses 3.45×10³ kg and 6.06×10⁴ kg are separated by a distance of 7,200 m. what is the gravitational force between the asteroids? newtons law of gravitation is (f_{gravity}=\frac{gm_1m_2}{r^2}). the gravitational constant g is 6.67×10⁻¹¹ n·m²/kg².
a. 4.03 n
b. 3.38×10³² n
c. 2.69×10⁻¹⁰ n
d. 1.93×10⁻⁶ n

Explanation:

Step1: Identify values

$G = 6.67\times 10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$, $m_1=3.45\times 10^{3}\text{ kg}$, $m_2 = 6.06\times 10^{4}\text{ kg}$, $r = 7200\text{ m}$

Step2: Substitute into formula

$F_{gravity}=\frac{Gm_1m_2}{r^{2}}=\frac{6.67\times 10^{-11}\times3.45\times 10^{3}\times6.06\times 10^{4}}{7200^{2}}$

Step3: Calculate numerator

$6.67\times 10^{-11}\times3.45\times 10^{3}\times6.06\times 10^{4}=(6.67\times3.45\times6.06)\times10^{-11 + 3+4}=138.77\times10^{-4}=1.3877$

Step4: Calculate denominator

$7200^{2}=7200\times7200 = 51840000$

Step5: Calculate force

$F_{gravity}=\frac{1.3877}{51840000}\approx 2.68\times 10^{-8}\approx2.69\times 10^{-10}\text{ N}$

Answer:

C. $2.69\times 10^{-10}\text{ N}$