If two objects each have the same mass m, separated by distance r, what happens to the gravitational force if you double both masses while keeping r constant?

If two objects each have the same mass m, separated by distance r, what happens to the gravitational force if you double both masses while keeping r constant?

• A. It doubles
• B. It halves
• C. It becomes four times smaller
• D. It becomes four times larger

Answer: (D)

Gravitational force scales with the product of the two masses when their separation is fixed: F ∝ m1 m2 / r^2. If both masses are doubled, the product m1 m2 becomes (2m)(2m) = 4m^2, so the force becomes four times larger. Since the distance is unchanged, the 1/r^2 factor stays the same. Therefore, the force increases by a factor of four.

Gravitational force scales with the product of the two masses when their separation is fixed: F ∝ m1 m2 / r^2. If both masses are doubled, the product m1 m2 becomes (2m)(2m) = 4m^2, so the force becomes four times larger. Since the distance is unchanged, the 1/r^2 factor stays the same. Therefore, the force increases by a factor of four.