Question

If Earth's radius were reduced by 1% while its mass remained unchanged, what would be the effect on the gravitational acceleration at its surface?

• A. Increase by approximately 1%
• B. Decrease by approximately 2%
• C. Increase by approximately 2%
• D. Decrease by approximately 1%

Answer 1

Answer:

C. Increase by approximately 2%

Gravitational Acceleration and Earth's Properties

Understanding the Formula

• The gravitational acceleration (g) at the surface of a celestial body is given by the formula: g = GM/R², where:

  • G is the universal gravitational constant.

  • M is the mass of the celestial body.

  • R is the radius of the celestial body.

Impact of Radius Change

• In this scenario, the Earth's mass (M) remains constant.

• The radius (R) is reduced by 1%. This means the new radius (R') is R' = R - 0.01R = 0.99R.

Calculating the New Gravitational Acceleration

• The new gravitational acceleration (g') can be calculated using the modified radius: g' = GM / (R')²

• Substitute R' = 0.99R: g' = GM / (0.99R)² = GM / (0.9801R²)

• We can rewrite this as: g' = (1 / 0.9801) * (GM / R²)

• Since g = GM/R², we have: g' = (1 / 0.9801) * g