Question

The force of gravity is an inverse square law. This means that, if you double the distance between two large masses, the gravitational force between them Group of answer choices weakens by a factor of 4. strengthens by a factor of 4. weakens by a factor of 2. also doubles. is unaffected.

Answer 1

Answer:

the force decreases by a factor of 4

Explanation:

The expression for the law of universal gravitation is

          F = $G \frac{m_1m_2}{r^2}$

let's call the force Fo for the distance r

          F₀ = $G \frac{m_1m_2}{r^2}$

They indicate that the distance doubles

          r ’= 2 r

we substitute

          F = $G \frac{m_1m_2}{(r')^2}$

          F = $G \frac{m_1m_2}{r^2} \ \frac{1}{4}$

         

          F = ¼ F₀

consequently the correct answer is that the force decreases by a factor of 4

Answer 2

If the distance between two large masses are doubled, the gravitational force between them weakens by a factor of 4.

Let the initial force be F

Let the initial distance apart be r

Thus, we can obtain the final force as follow:

Initial force (F₁) = F

Initial distance apart (r₁) = r

Final distance apart (r₂) = 2r

Final force (F₂) =?

F = GM₁M₂ / r²

Fr² = GM₁M₂ (constant)

Thus,

F₁r₁² = F₂r₂²

Fr² = F₂(2r)²

Fr² = F₂4r²

Divide both side by 4r²

F₂ = Fr² /4r²

F₂ = F / 4

From the illustration above, we can see that when the distance (r) is doubled, the force (F) is decreased (i.e weakens) by a factor of 4

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