Two spheres are placed so that their centers are 2.6 m apart. The force between the two spheres is 2.70 ✕ 10-12 N. What is the mass of each sphere if one sphere is twice the mass of the other sphere?

0.37 kg and 0.74 kg

Explanation:

From Newton's law of universal gravitation,

F = Gm'm/r² ... Equation 1.

Where F = force, m' = mass of the first sphere, m = mass of the second sphere, r = distance between the center of the sphere, G = universal gravitational constant.

Given: F = 2.7*10⁻¹² N, r = 2.6 m,

Constant: G = 6.67*10⁻¹¹ Nm²/kg²

Let: m' = y kg, the m' = 2y kg

Substitute these values into equation 1

2.7*10⁻¹² = 6.67*10⁻¹¹ (y*2y) / 2.6²

2.7*10⁻¹² = 6.67*10⁻¹¹ (2y²) / 6.76

y² = (0.27*6.76) / (6.67*2)

y² = 0.137

y = √0.137

y = 0.37 kg.

m' = 0.37 kg, m = 2*0.37 = 0.74 kg.

Hence the masses are 0.37 kg and 0.74 kg