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If the radius of the Earth were to increase while keeping its mass constant, wha

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Question: If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at its surface?

Options:

  1. It increases
  2. It decreases
  3. It remains the same
  4. It becomes zero

Correct Answer: It decreases

Solution: 

Gravitational acceleration g = GM/R². If R increases, g decreases.

If the radius of the Earth were to increase while keeping its mass constant, wha

Practice Questions

Q1
If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at its surface?
  1. It increases
  2. It decreases
  3. It remains the same
  4. It becomes zero

Questions & Step-by-Step Solutions

If the radius of the Earth were to increase while keeping its mass constant, what would happen to the gravitational acceleration at its surface?
  • Step 1: Understand that gravitational acceleration (g) depends on two things: the mass of the Earth (M) and the radius of the Earth (R).
  • Step 2: Recall the formula for gravitational acceleration: g = GM/R², where G is the gravitational constant.
  • Step 3: Note that if the radius (R) of the Earth increases while the mass (M) stays the same, the value of R in the formula becomes larger.
  • Step 4: Since R is in the denominator (the bottom part) of the formula, making R larger will make the overall value of g smaller.
  • Step 5: Conclude that if the radius of the Earth increases and mass remains constant, the gravitational acceleration (g) at the surface will decrease.
  • Gravitational Acceleration – The relationship between gravitational acceleration, mass, and radius as described by the formula g = GM/R².
  • Inverse Square Law – Understanding how changes in radius affect gravitational force due to the inverse square relationship.
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