A new planet has twice Earth’s mean density but the same surface acceleration due to gravity. If Earth has radius R, the new planet’s radius is:
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Question

A new planet has twice Earth’s mean density but the same surface acceleration due to gravity. If Earth has radius R, the new planet’s radius is:

G1 Physics · Accepted Answer

Step 1: Using g=(4π/3)GρR, equality of gravity gives ρₚRₚ=ρₑR. Step 2: With ρₚ=2ρₑ, Rₚ=R/2. Final answer: D — R/2.