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:
Show Hint
- 5.6
- 2.8
- 11.2
- 8.4
The Correct Option is A
Solution and Explanation
The escape velocity is given by the formula: \[ v_{escape} = \sqrt{\frac{2GM}{R}} \]
Step 2: Given Mass and Radius RelationshipsWe are given the following mass and radius relationships: \[ \frac{M_{planet}}{M_{earth}} = \frac{1}{8}, \quad \frac{R_{planet}}{R_{earth}} = \frac{1}{2} \]
Step 3: Calculate the Ratio of Escape VelocitiesThe ratio of the escape velocities is: \[ \frac{v_{escape, planet}}{v_{escape, earth}} = \sqrt{\frac{M_{planet} R_{earth}}{M_{earth} R_{planet}}} = \frac{1}{2} \]
Step 4: Calculate the Escape Velocity from the PlanetTherefore, the escape velocity from the planet is: \[ v_{escape, planet} = \frac{1}{2} \times 11.2 = 5.6 \, \text{km/s} \]
Final Answer: \[ v_{escape, planet} = 5.6 \, \text{km/s} \]Learn with videos:
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