If the Earth were to suddenly shrink to half its radius while keeping its mass constant, what would happen to the gravitational force at its surface?
Practice Questions
1 question
Q1
If the Earth were to suddenly shrink to half its radius while keeping its mass constant, what would happen to the gravitational force at its surface?
It would remain the same
It would double
It would become half
It would become four times stronger
If the radius is halved, the gravitational force increases by a factor of 4, since F = GM/R^2.
Questions & Step-by-step Solutions
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Q
Q: If the Earth were to suddenly shrink to half its radius while keeping its mass constant, what would happen to the gravitational force at its surface?
Solution: If the radius is halved, the gravitational force increases by a factor of 4, since F = GM/R^2.
Steps: 6
Step 1: Understand the formula for gravitational force, which is F = GM/R^2, where F is the gravitational force, G is the gravitational constant, M is the mass, and R is the radius.
Step 2: Note that if the Earth shrinks to half its radius, the new radius R' will be R/2.
Step 3: Substitute the new radius into the formula: F' = GM/(R/2)^2.
Step 4: Simplify the equation: F' = GM/(R^2/4) = GM * (4/R^2).
Step 5: This shows that the new gravitational force F' is 4 times the original gravitational force F, since F' = 4F.
Step 6: Conclude that if the radius is halved, the gravitational force at the surface increases by a factor of 4.
