Question

Two objects placed a distance r apart have a gravitational force of F between them. Give the magnitude of the new force (in terms of F) if the:

(a) Mass of both objects is halved
A) F/2
B) F
C) 2F
D) 4F

Answer 1

The gravitational force F becomes F/4 when the mass of both objects is halved because the gravitational force is proportional to the product of the two masses. Multiplying each mass by 1/2 results in the force becoming (1/2)^2 times the original, which is 1/4 of the original force F.

Step-by-step explanation:

The question involves understanding the gravitational force between two objects, which can be described by Newton's universal law of gravitation:

F = G M₁ M₂ / r²

where G is the gravitational constant, M₁ and M₂ are the masses of the two bodies, and r is the distance between them.

If the mass of both objects is halved, the new masses become M₁/2 and M₂/2. When you plug these values into the equation, you get:

F' = G (M₁/2) (M₂/2) / r² = (1/2²) (G M₁ M₂ / r²) = (1/4)F

Therefore, the new force F' after halving the mass of both objects would be F/4. So the correct answer is D) 4F, which is actually one fourth of the original force, not four times.