The escape velocities of planets A and B are in the ratio 1:2. Their radii are in the ratio Rₐ: Rʙ = 1:3. The ratio gₐ: gʙ is:
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Question

The escape velocities of planets A and B are in the ratio 1:2. Their radii are in the ratio Rₐ:Rʙ = 1:3. The ratio gₐ:gʙ is:

G1 Physics · Accepted Answer

Using: vₑ = √(2gR) Therefore: (vₑₐ/vₑʙ)² = (gₐRₐ)/(gʙRʙ) Given: vₑₐ/vₑʙ = 1/2 Rₐ/Rʙ = 1/3 1/4 = (gₐ/gʙ)(1/3) gₐ/gʙ = 3/4 Hence option D.