Question

The gravitational force between two asteroids is 6. 2 × 108 N. Asteroid Y has three times the mass of asteroid Z. If the distance between the asteroids is 2100 kilometers, what is the mass of asteroid Y? 3. 7 × 1015 kg 1. 1 × 1016 kg 1. 4 × 1031 kg 4. 1 × 1031 kg.

Answer 1

Answer:Let m = mass of asteroid y.Because asteroid y has three times the mass of asteroid z, the mass of asteroid z is m/3.Given:F = 6.2x10⁸ Nd = 2100 km = 2.1x10⁶ mNote thatG = 6.67408x10⁻¹¹ m³/(kg-s²)The gravitational force between the asteroids isF = (G*m*(m/3))/d² = (Gm²)/(3d²)orm² = (3Fd²)/G = [(3*(6.2x10⁸ N)*(2.1x10⁶ m)²]/(6.67408x10⁻¹¹ m³/(kg-s²)) = 1.229x10³² kg²m = 1.1086x10¹⁶ kg = 1.1x10¹⁶ kg (approx)Answer: 1.1x10¹⁶ kg

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