If the distance from the center of the Earth is doubled, what happens to the gravitational field strength?
Practice Questions
1 question
Q1
If the distance from the center of the Earth is doubled, what happens to the gravitational field strength?
It doubles.
It halves.
It becomes one-fourth.
It becomes zero.
The gravitational field strength varies inversely with the square of the distance from the center of the Earth, so if the distance is doubled, the field strength becomes one-fourth.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance from the center of the Earth is doubled, what happens to the gravitational field strength?
Solution: The gravitational field strength varies inversely with the square of the distance from the center of the Earth, so if the distance is doubled, the field strength becomes one-fourth.
Steps: 7
Step 1: Understand that gravitational field strength is how strong gravity is at a certain distance from the center of the Earth.
Step 2: Know that the formula for gravitational field strength (g) is g = G * (M / r^2), where G is a constant, M is the mass of the Earth, and r is the distance from the center of the Earth.
Step 3: Recognize that if the distance (r) is doubled, we replace r with 2r in the formula.
Step 4: Calculate the new gravitational field strength: g' = G * (M / (2r)^2).
Step 5: Simplify the equation: g' = G * (M / (4r^2)).
Step 6: Notice that g' is one-fourth of the original gravitational field strength (g), because the denominator has increased by a factor of 4.
Step 7: Conclude that if the distance from the center of the Earth is doubled, the gravitational field strength becomes one-fourth.
