MCQ Detailed View

Escape velocity is the minimum speed an object must reach to overcome Earth's gravitational pull and move away indefinitely without further propulsion. This value is determined by the planet's mass and radius, and for Earth, the escape velocity is approximately 11.2 kilometers per second (km/s).

The formula for escape velocity is:

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

Where:

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  $G$ = universal gravitational constant (6.674×10−11 Nm2/kg26.674 \times 10^{-11} \, Nm^2/kg^26.674×10−11Nm2/kg2)

  
  


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  $M$ = mass of the Earth (5.97×1024 kg5.97 \times 10^{24} \, kg5.97×1024kg)

  
  


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  $R$ = radius of the Earth (~6,371 km)

  
  

Plugging in these values gives:

ve=2×6.674×10−11×5.97×10246.371×106≈11,200 m/s=11.2 km/sv_e = \sqrt{\frac{2 \times 6.674 \times 10^{-11} \times 5.97 \times 10^{24}}{6.371 \times 10^{6}}} \approx 11,200 \, m/s = 11.2 \, km/sve=6.371×1062×6.674×10−11×5.97×1024≈11,200m/s=11.2km/s

This means any object—whether a spacecraft or a piece of rock—must reach 11.2 km/s (about 40,320 km/h) at Earth's surface to completely escape its gravitational field, neglecting atmospheric resistance.

Key facts:

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  7.9 km/s is the orbital velocity needed for a stable low Earth orbit, not escape velocity.

  
  


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  9.8 m/s² is the acceleration due to gravity on Earth, not a speed.

  
  


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  12.4 km/s exceeds the required value.

  
  

Escape velocity does not depend on the object's mass, only on Earth's mass and radius. This principle is vital in astronomy and space travel, as it determines the amount of energy rockets need to leave Earth's gravitational influence.

✅ Correct Answer: 11.2 km/s.