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?

• A. 22.4 km/s
• B. 7.9 km/s
• C. 15.8 km/s
• D. 5.6 km/s

Hint:

Escape velocity is inversely proportional to the square root of the radius if the mass is constant: \[ v_e \propto \frac{1}{\sqrt{R}} \]

Answer 1

The Correct Option is B

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: \[ v_e' = \frac{11.2}{\sqrt{2}} \approx \frac{11.2}{1.414} \approx 7.92 \, \text{km/s} \approx 7.9 \, \text{km/s} \]