Question

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

• A. 5.6
• B. 2.8
• C. 11.2
• D. 8.4

Hint:

Escape velocity depends on both the mass and radius of the planet or celestial body. A smaller mass and radius result in a lower escape velocity.

Answer 1

The Correct Option is A

The formula for escape velocity is: \[v_{escape} = \sqrt{\frac{2GM}{R}}\] The mass and radius relationships are provided as: \[\frac{M_{planet}}{M_{earth}} = \frac{1}{8}, \quad \frac{R_{planet}}{R_{earth}} = \frac{1}{2}\] Consequently, the ratio of escape velocities is calculated as: \[\frac{v_{escape, planet}}{v_{escape, earth}} = \sqrt{\frac{M_{planet} R_{earth}}{M_{earth} R_{planet}}} = \frac{1}{2}\] This leads to the escape velocity from the planet being: \[v_{escape, planet} = \frac{1}{2} \times 11.2 = 5.6 \, {km/s}\]