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If the radius of the Earth were to increase by a factor of 2, what would happen

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Question: If the radius of the Earth were to increase by a factor of 2, what would happen to the gravitational acceleration at its surface?

Options:

  1. It would double
  2. It would remain the same
  3. It would halve
  4. It would become one-fourth

Correct Answer: It would halve

Solution: 

Gravitational acceleration is inversely proportional to the square of the radius. If the radius doubles, g becomes 1/(2^2) = 1/4 of the original value.

If the radius of the Earth were to increase by a factor of 2, what would happen

Practice Questions

Q1
If the radius of the Earth were to increase by a factor of 2, what would happen to the gravitational acceleration at its surface?
  1. It would double
  2. It would remain the same
  3. It would halve
  4. It would become one-fourth

Questions & Step-by-Step Solutions

If the radius of the Earth were to increase by a factor of 2, what would happen to the gravitational acceleration at its surface?
  • Step 1: Understand that gravitational acceleration (g) depends on the mass of the Earth and the distance from its center (radius).
  • Step 2: Know that if the radius of the Earth increases, the distance from the center to the surface increases.
  • Step 3: Remember the formula for gravitational acceleration: g = G * M / r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the radius.
  • Step 4: If the radius (r) doubles, we replace r with 2r in the formula: g = G * M / (2r)^2.
  • Step 5: Calculate (2r)^2, which equals 4r^2.
  • Step 6: Substitute this back into the formula: g = G * M / 4r^2.
  • Step 7: Notice that this means g is now 1/4 of what it was before because we have divided by 4.
  • Step 8: Conclude that if the radius of the Earth doubles, the gravitational acceleration at its surface becomes 1/4 of the original value.
  • Gravitational Acceleration – Gravitational acceleration at the surface of a planet is determined by the mass of the planet and the distance from its center, following the formula g = G * M / r^2.
  • Inverse Square Law – The gravitational force and acceleration are inversely proportional to the square of the distance from the center of the mass.
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