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What is the escape velocity from the surface of a planet with a radius of 4,000

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Question: What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)

Options:

  1. 10,000 m/s
  2. 11,200 m/s
  3. 12,000 m/s
  4. 13,000 m/s

Correct Answer: 11,200 m/s

Solution: 

Escape velocity = √(2GM/R) = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6) = 11,200 m/s

What is the escape velocity from the surface of a planet with a radius of 4,000

Practice Questions

Q1
What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)
  1. 10,000 m/s
  2. 11,200 m/s
  3. 12,000 m/s
  4. 13,000 m/s

Questions & Step-by-Step Solutions

What is the escape velocity from the surface of a planet with a radius of 4,000 km and a mass of 6 × 10^24 kg? (G = 6.67 × 10^-11 N m²/kg²)
  • Step 1: Identify the formula for escape velocity, which is Escape velocity = √(2GM/R).
  • Step 2: Identify the values needed for the formula: G = 6.67 × 10^-11 N m²/kg², M = 6 × 10^24 kg, and R = 4,000 km (which needs to be converted to meters).
  • Step 3: Convert the radius from kilometers to meters: 4,000 km = 4 × 10^6 m.
  • Step 4: Substitute the values into the formula: Escape velocity = √(2 * 6.67 × 10^-11 * 6 × 10^24 / 4 × 10^6).
  • Step 5: Calculate the numerator: 2 * 6.67 × 10^-11 * 6 × 10^24 = 8.004 × 10^{14}.
  • Step 6: Divide the result by the radius: 8.004 × 10^{14} / 4 × 10^6 = 2.001 × 10^{8}.
  • Step 7: Take the square root of the result: √(2.001 × 10^{8}) = 11,200 m/s.
  • Step 8: Conclude that the escape velocity from the surface of the planet is 11,200 m/s.
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