If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?
Practice Questions
1 question
Q1
If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?
It would double
It would remain the same
It would be halved
It would be quartered
Gravitational acceleration is inversely proportional to the square of the radius, so it would be quartered.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of the Earth were to double, what would happen to the gravitational acceleration at its surface?
Solution: Gravitational acceleration is inversely proportional to the square of the radius, so it would be quartered.
Steps: 7
Step 1: Understand that gravitational acceleration (g) depends on the mass of the Earth 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 of the Earth, and r is the radius of the Earth.
Step 3: Note that if the radius (r) doubles, it becomes 2r.
Step 4: Substitute 2r into the formula: g = G * (M / (2r)^2).
Step 5: Simplify the equation: (2r)^2 = 4r^2, so g = G * (M / 4r^2).
Step 6: This shows that the new gravitational acceleration is g/4, meaning it is one-fourth of the original value.
Step 7: Conclude that if the radius of the Earth doubles, the gravitational acceleration at its surface would be quartered.
