MCQ Detailed View

Escape velocity is the minimum speed an object must achieve to completely overcome a planet's gravitational pull and move into space without further propulsion. For Earth, this value is about 11.2 km/s, calculated using the formula:

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

Where:

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  $G$ = universal gravitational constant

  
  


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  $M$ = mass of Earth

  
  


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  $R$ = radius of Earth

  
  

From this equation, we see that escape velocity depends only on the planet's mass (M) and radius (R), not on the mass of the object trying to escape. This means whether the object is a small pen or a large house, the minimum escape speed required is exactly the same under ideal conditions.Gravitational force indeed depends on the object's mass (more mass → more gravitational force), but at the same time, the kinetic energy of a heavier object is also higher for the same speed. These effects cancel out mathematically, making escape velocity independent of the escaping object’s mass.

Key facts:

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  Both a pen and a home need 11.2 km/s on Earth to break free from gravity.

  
  


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  Larger mass does not require a higher escape speed but does require more energy (since energy = ½ mv²).

  
  


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  Air resistance and practical engineering factors can differ, but in ideal physics, the required speed remains the same.

  
  

Hence, the correct answer is:

✅ Both need the same velocity.