Answer:
0.37 kg and 0.74 kg
Step-by-step 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