Question

Two objects attract each other with a gravitational force of magnitude 1.00 10-8 N when separated by 19.3 cm. If the total mass of the objects is 5.05 kg, what is the mass of each?

Answer 1

$F = 1.0 \times 10^{-8} \;N \\ r = 19.3 \times 10^{-2} \;m \\ m_1+m_2=5.05$

From Newton’s law of force

$F = \frac{Gm_1m_2}{r^2} \\ 1.0 \times 10^{-8} = \frac{6.67 \times 10^{-11} \times m_1m_2}{(19.3 \times 10^{-2})^2} \\ 5.584 = m_1m_2 \\ m_1+m_2=5.05 \\ m_1 = 5.05 -m_2 \\ 5.584 = (5.05 -m_2)m_2 \\ 5.584 = 5.05m_2 -m_2^2 \\ m^2_2 -5.05m_2 + 5.584 = 0 \\ m_2 = 3.41 \\ m_1 = 1.64$