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If the radius of a planet is halved, what happens to the gravitational accelerat
If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?
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Practice Questions
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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
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g ∝ 1/R². If R is halved, g becomes 4 times greater.
Questions & Step-by-step Solutions
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Q
Q: If the radius of a planet is halved, what happens to the gravitational acceleration on its surface?
Solution:
g ∝ 1/R². If R is halved, g becomes 4 times greater.
Steps: 6
Show Steps
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.
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