How does the gravitational force between two objects change if both masses are doubled?
Practice Questions
1 question
Q1
How does the gravitational force between two objects change if both masses are doubled?
It becomes four times stronger
It becomes twice as strong
It remains the same
It becomes half as strong
Doubling both masses results in a fourfold increase in gravitational force, as it is directly proportional to the product of the masses.
Questions & Step-by-step Solutions
1 item
Q
Q: How does the gravitational force between two objects change if both masses are doubled?
Solution: Doubling both masses results in a fourfold increase in gravitational force, as it is directly proportional to the product of the masses.
Steps: 7
Step 1: Understand that gravitational force depends on the masses of the two objects and the distance between them.
Step 2: Recall the formula for gravitational force: F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Step 3: If both masses (m1 and m2) are doubled, we can write the new masses as 2*m1 and 2*m2.
Step 4: Substitute the new masses into the formula: F' = G * (2*m1 * 2*m2) / r^2.
Step 5: Simplify the equation: F' = G * (4*m1*m2) / r^2.
Step 6: Notice that F' is four times the original force (F), since F = G * (m1 * m2) / r^2.
Step 7: Conclude that doubling both masses results in a fourfold increase in gravitational force.
