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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 the surface? (2023)

Options:

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

Correct Answer: It decreases

Exam Year: 2023

Solution: 

Gravitational acceleration is inversely proportional to the square of the radius. If radius 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 the surface? (2023)
  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 the surface? (2023)
  • Step 1: Understand that gravitational acceleration (g) is affected by the mass of an object and the distance from its center (radius).
  • Step 2: Recall the formula for gravitational acceleration: g = G * (M / R^2), where G is the gravitational constant, M is the mass, and R is the radius.
  • Step 3: Note that in this scenario, the mass (M) of the Earth remains constant.
  • Step 4: Recognize that if the radius (R) of the Earth increases, the value of R^2 (the radius squared) also increases.
  • Step 5: Since g is inversely proportional to R^2, an increase in R^2 means that g will decrease.
  • Step 6: Conclude that if the radius of the Earth increases while keeping its mass constant, the gravitational acceleration at the surface will decrease.
  • Gravitational Acceleration – Gravitational acceleration (g) is determined by the formula g = G * M / r^2, where G is the gravitational constant, M is the mass of the object, and r is the radius from the center of the mass to the point where g is being measured.
  • Inverse Square Law – The gravitational force and acceleration are inversely proportional to the square of the distance (radius) from the center of the mass, meaning that as the radius increases, the gravitational acceleration decreases.
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