Question

A heavier mass m₁ and a lighter mass m₂ are 18.5 cm apart and experience a gravitational force of attraction that is 8.80 x 10⁻⁹ N in magnitude. The two masses have a combined value of 5.40 kg. Determine the value of each individual mass.
m₁ = ____ kg
m₂ = ____ kg

Answer 1

m₁ is 4.37 kg and m₂ is 1.03 kg

Explanation:

Sum of masses = m₁ + m₂ = 5.40 kg

                             m₂ = 5.4 - m₁

We have gravitational force

              $F=\frac{Gm_1m_2}{r^2}$

         G = 6.674 x 10⁻¹¹ Nm²/kg²

          r = 18.5 cm = 0.185 m

          F = 8.80 x 10⁻⁹ N

Substituting,

              $8.8\times 10^{-9}=\frac{6.674\times 10^{-11}m_1m_2}{0.185^2}\\\\m_1m_2=4.513$

               m₁ x (5.4-m₁) = 4.513

                5.4m₁ - m₁² = 4.513

               m₁² - 5.4m₁ + 4.513 = 0

               m₁ = 4.37kg    or     m₁ = 1.03 kg

       If  m₁ = 4.37 kg   we have

                      m₂ = 1.03 kg    

       If  m₁ = 1.03 kg   we have

                      m₂ =  4.37 kg    

So Let us consider

          m₁ = 4.37 kg and m₂ = 1.03 kg