How does the gravitational force between two objects change if both masses are d

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Question: How does the gravitational force between two objects change if both masses are doubled?

Options:

Correct Answer: It becomes four times stronger

Solution:

Doubling both masses results in a fourfold increase in gravitational force, as it is directly proportional to the product of the masses.

How does the gravitational force between two objects change if both masses are doubled?

How does the gravitational force between two objects change if both masses are doubled?

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.

Gravitational Force – The gravitational force between two objects is calculated using Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
Proportionality – Understanding how changes in mass affect the gravitational force, specifically that if both masses are doubled, the force increases by a factor of four.