Planets P₁ and P₂ have equal masses and radii R₁ and R₂, with R₂ = R₁/2. If their escape speeds are v₁ and v₂, find v₂/v₁.
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Question

Planets P₁ and P₂ have equal masses and radii R₁ and R₂, with R₂ = R₁/2. If their escape speeds are v₁ and v₂, find v₂/v₁.

G1 Physics · Accepted Answer

Step 1: Escape speed from a planet's surface is vₑ = √(2GM/R). Step 2: For equal planet masses, vₑ ∝ 1/√R. Step 3: Thus v₂/v₁ = √(R₁/R₂) = √(R₁/(R₁/2)) = √2. Final answer: √2 (Option C).