An astronaut on a newly discovered planet drops a small 2 kg sphere from a height of 20 m. It takes exactly 4 seconds to hit the ground. The planet is perfectly spherical with a radius equal to half of the Earth's radius. Assuming no air resistance, what is the ratio of the mass of the planet to the mass of the Earth? (Take g on Earth = 10 m/s²)

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• A 1 : 16
• B 1 : 8
• C 1 : 4
• D 1 : 2

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Answer: A. 1 : 16

h = (1/2)gt², so 20 = (1/2) × g × 16 and g on the planet = 2.5 m/s².
g = GM/R², so M is proportional to gR².
M(planet)/M(Earth) = (2.5/10) × (0.5)² = 1/4 × 1/4 = 1/16.

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