Question

A planet is 121 times heavier than moon and has a diameter 9 times that of moon. If the escape velocity on the planet is \(v\), then the escape velocity on the moon will be:

• A. \( \frac{11v}{3} \)
• B. \( \frac{3v}{11} \)
• C. \( \frac{8v}{33} \)
• D. \( \frac{3v}{11} \)

Hint:

Escape velocity depends on \( \sqrt{\frac{M}{R}} \). Always take ratio carefully using both mass and radius.

Answer 1

The Correct Option is D

Step 1: Formula for escape velocity.
\[ v_e = \sqrt{\frac{2GM}{R}} \]

Step 2: Write ratio for planet and moon.
\[ \frac{v_p}{v_m} = \sqrt{\frac{M_p / R_p}{M_m / R_m}} \]

Step 3: Substitute given ratios.
\[ M_p = 121 M_m, \quad R_p = 9 R_m \]
\[ \frac{v_p}{v_m} = \sqrt{\frac{121/9}{1}} = \sqrt{\frac{121}{9}} \]

Step 4: Simplify.
\[ \frac{v_p}{v_m} = \frac{11}{3} \]

Step 5: Express moon velocity.
\[ v_m = \frac{3}{11} v_p \]

Step 6: Final conclusion.
\[ \boxed{\frac{3v}{11}} \] Hence, correct answer is option (D).