Question

The escape velocity from the surface of earth of mass \( M \) and radius \( R \) is \( V_e \). The escape velocity from the surface of a planet whose mass and radius are 3 times that of the earth will be

• A. \( 9V_e \)
• B. \( 3V_e \)
• C. \( V_e \)
• D. \( 12V_e \)

Hint:

If mass and radius increase in the same ratio, escape velocity remains the same.

Answer 1

The Correct Option is C

Step 1: Write formula for escape velocity.
\[ V_e = \sqrt{\frac{2GM}{R}} \]
Step 2: Substitute new mass and radius.
For the planet: \[ M' = 3M,\quad R' = 3R \]
Step 3: Calculate new escape velocity.
\[ V'_e = \sqrt{\frac{2G(3M)}{3R}} = \sqrt{\frac{2GM}{R}} = V_e \]
Step 4: Conclusion.
The escape velocity remains unchanged.