MCQ Detailed View

Escape velocity is defined as the minimum speed an object needs to overcome a planet’s gravitational pull and move away indefinitely, without requiring additional propulsion. 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

  
  


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  $R$ = radius of the planet

  
  

From this formula, we can understand the factors that affect escape velocity:

1️⃣ Mass of the Planet:
Escape velocity depends directly on the mass of the planet. The greater the mass, the stronger its gravity, hence a higher velocity is needed to escape.

2️⃣ Mass of the Escaping Object:
Escape velocity is independent of the mass of the escaping object. Whether it is a small satellite or a large spaceship, as long as friction is neglected, both need the same minimum speed to escape the planet’s gravitational field.

3️⃣ Radius of the Planet:
Escape velocity is inversely proportional to the square root of the radius. If the planet’s radius increases while its mass remains constant, the gravitational pull becomes weaker, requiring a lower escape velocity.

4️⃣ Shape of the Planet:
Escape velocity does not depend on the shape of the planet but only on its total mass and radius.

Thus, the correct statement is that escape velocity is independent of the mass of the escaping object. This is why all objects, regardless of their size, require the same escape speed to leave a planet’s gravitational influence under ideal conditions.

✅ Correct Answer: Escape velocity is independent of the mass of the escaping object.