If the distance from the center of the Earth is doubled, what happens to the gra
Practice Questions
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.
Questions & Step-by-Step Solutions
If the distance from the center of the Earth is doubled, what happens to the gravitational field strength?
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.
Gravitational Field Strength – The gravitational field strength is the force experienced by a unit mass at a point in a gravitational field, which decreases with the square of the distance from the mass creating the field.
Inverse Square Law – This law states that the strength of a gravitational field decreases with the square of the distance from the center of the mass, meaning if the distance is doubled, the field strength is reduced to one-fourth.
