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

Step 1: Escape Velocity Formula Provided

The formula for escape velocity is: \[ v_{escape} = \sqrt{\frac{2GM}{R}} \]

Step 2: Mass and Radius Ratios Given

The following relationships for mass and radius are provided: \[ \frac{M_{planet}}{M_{earth}} = \frac{1}{8}, \quad \frac{R_{planet}}{R_{earth}} = \frac{1}{2} \]

Step 3: Escape Velocity Ratio Calculation

The ratio of the escape velocities is calculated as: \[ \frac{v_{escape, planet}}{v_{escape, earth}} = \sqrt{\frac{M_{planet} R_{earth}}{M_{earth} R_{planet}}} = \frac{1}{2} \]

Step 4: Planet's Escape Velocity Calculation

Consequently, the escape velocity from the planet is: \[ v_{escape, planet} = \frac{1}{2} \times 11.2 = 5.6 \, \text{km/s} \]

Final Answer: \[ v_{escape, planet} = 5.6 \, \text{km/s} \]