Question:
The escape velocity from the surface of a planet is 11.2 km/s. If the radius of the planet is doubled but the mass remains the same, what will be the new escape velocity?
The escape velocity from the surface of a planet is 11.2 km/s. If the radius of the planet is doubled but the mass remains the same, what will be the new escape velocity?
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Escape velocity is inversely proportional to the square root of the radius if the mass is constant:
\[
v_e \propto \frac{1}{\sqrt{R}}
\]
Updated On: Jan 13, 2026
- 22.4 km/s
- 7.9 km/s
- 15.8 km/s
- 5.6 km/s
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Recall the escape velocity formula. \[ v_e = \sqrt{\frac{2GM}{R}} \] Step 2: When radius is doubled (i.e., \( R \rightarrow 2R \)) and mass remains the same: \[ v_e' = \sqrt{\frac{2GM}{2R}} = \sqrt{\frac{1}{2}} \cdot \sqrt{\frac{2GM}{R}} = \frac{v_e}{\sqrt{2}} \] Step 3: Compute new velocity: \[ v_e' = \frac{11.2}{\sqrt{2}} \approx \frac{11.2}{1.414} \approx 7.92 \, \text{km/s} \approx 7.9 \, \text{km/s} \]
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