Question: If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?
Options:
It doubles
It halves
It becomes one-fourth
It remains the same
Correct Answer: It doubles
Solution:
g ∝ 1/R². If R is halved, g becomes 4 times greater.
If the radius of a planet is halved, what happens to the gravitational accelerat
Practice Questions
Q1
If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?
It doubles
It halves
It becomes one-fourth
It remains the same
Questions & Step-by-Step Solutions
If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?
Step 1: Understand that gravitational acceleration (g) is related to the radius (R) of the planet.
Step 2: Remember the formula that shows this relationship: g is proportional to 1 divided by the square of the radius (g ∝ 1/R²).
Step 3: If the radius (R) is halved, we can express this as R = R/2.
Step 4: Substitute R/2 into the formula: g ∝ 1/(R/2)².
Step 5: Simplify the equation: (R/2)² = R²/4, so g ∝ 1/(R²/4) = 4/R².
Step 6: This means that if the radius is halved, the gravitational acceleration (g) becomes 4 times greater.
Gravitational Acceleration – The relationship between gravitational acceleration and the radius of a planet, specifically that gravitational acceleration is inversely proportional to the square of the radius.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
