MCQ Detailed View

Escape velocity is defined as the minimum speed an object needs to break free from a planet or celestial body’s gravitational field without requiring further propulsion. It is a fundamental concept in physics, especially in astronomy and space exploration.

The formula for escape velocity is:

ve=2GMRv_e = \sqrt{\frac{2GM}{R}}ve=R2GM

Where:

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  vev_eve = escape velocity

  
  


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  $G$ = universal gravitational constant

  
  


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  $M$ = mass of the planet or celestial body

  
  


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  $R$ = radius of the planet or celestial body

  
  

From this formula, it is clear that escape velocity depends on two factors:

1️⃣ Mass of the planet or celestial body (M):
The larger the mass, the stronger its gravitational pull. A greater gravitational force requires a higher velocity to escape. For example, Jupiter, being more massive than Earth, has a much higher escape velocity (~59.5 km/s) compared to Earth (~11.2 km/s).

2️⃣ Radius of the planet or celestial body (R):
Escape velocity is inversely proportional to the square root of the radius. If the radius is larger (with the same mass), the gravitational pull at the surface is weaker, and less velocity is required to escape.

Escape velocity does not depend on:

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  The mass of the object trying to escape: Whether it’s a satellite or a spaceship, both need the same escape velocity under ideal conditions.

  
  


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  The rotational speed of the planet: While rotation slightly affects trajectories, it does not change the fundamental escape velocity.

  
  

Therefore, the correct choice is that escape velocity depends on both the mass and the radius of the planet or celestial body.

✅ Correct Answer: Both mass and radius of the planet or celestial body.