Question

A planet in a distant solar system is 10 times more massive than Earth and its radius is 10 times smaller. Given that the escape velocity from Earth's surface is 11 km/s, the escape velocity from the planet’s surface would be:

• A. \( 1.1 \) km/s
• B. \( 11 \) km/s
• C. \( 110 \) km/s
• D. \( 0.11 \) km/s

Hint:

Escape velocity scales as \( \sqrt{M/R} \). Larger mass and smaller radius increase escape velocity.

Answer 1

The Correct Option is C

Step 1: Escape velocity is given by: \[ v_e = \sqrt{\frac{2GM}{R}} \] If mass is 10 times greater and radius is 10 times smaller, we get: \[ v'_e = \sqrt{\frac{2G(10M)}{R/10}} = \sqrt{100} v_e = 10 v_e \] Step 2: Since \( v_e = 11 \) km/s, we get: \[ v'_e = 10 \times 11 = 110 { km/s} \]