The escape velocities of planets A and B are in the ratio 1:2. Their radii are in the ratio $R_{A}\colon R_{B}$ = 1:3. The ratio $\frac{g_{A}}{g_{B}}$ 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 $R_{A}\colon R_{B}$ = 1:3. The ratio $\frac{g_{A}}{g_{B}}$ is:

Options

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 \frac{3}{4} 4 3 ​ Hence option D.

The escape velocities of planets A and B are in the ratio 1:2. Their radii are in the ratio R A ⁣ : R B R_{A}\colon R_{B} R A ​ : R B ​ = 1:3. The ratio g A g B \frac{g_{A}}{g_{B}} g B ​ g A ​ ​ is:

The escape velocities of planets A and B are in the ratio 1:2. Their radii are in the ratio R A ⁣ : R B R_{A}\colon R_{B} R A : R B = 1:3. The ratio g A g B \frac{g_{A}}{g_{B}} g B g A is: