How would the force of gravity between two objects change if the mass of each object were doubled?
A. The force between them would be 2 times larger than with the
initial masses.
B. The force between them would be 1/4 the force with the initial
separation.
C. The force between them would be 4 times larger than with the
initial masses.
D. The force between them would be 1/2 the force with the initial
separation

Option C. The force between them would be 4 times larger than with the

initial masses.

Explanation:

To know which option is correct, we shall determine the force of attraction between the two masses when their masses are doubled. This can be obtained as follow:

From:

F = GMₐM₆/ r²

Keeping G/r² constant, we have

F₁ = MₐM₆

Let the initial mass of both objects to be m

F₁ = MₐM₆

F₁ = m × m

F₁ = m²

Next, let the masses of both objects doubles i.e 2m

F₂ = MₐM₆

F₂ = 2m × 2m

F₂ = 4m²

Compare the initial and final force

Initial force (F₁) = m²

Final (F₂) = 4m²

F₂ / F₁ = 4m² / m²

F₂ / F₁ = 4

F₂ = 4F₁ = 4m²

From the above illustrations, we can see that when the mass of both objects doubles, the force between them would be 4 times larger than with the

initial masses.

Thus, option C gives the correct answer to the question.

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.