If the distance between two objects decreases to 1/2 of its original distance, then the gravitational force between the two objects will ___________ its original value.[Hint: What happened when Yoda got closer to R2?] Group of answer choicesdecrease to 1/4decrease to 1/2remain the same asincrease by 2xincrease by 4x
Question
If the distance between two objects decreases to 1/2 of its original distance, then the gravitational force between the two objects will ___________ its original value.[Hint: What happened when Yoda got closer to R2?] Group of answer choicesdecrease to 1/4decrease to 1/2remain the same asincrease by 2xincrease by 4x
Solution
The gravitational force between two objects is given by the formula:
F = G * (m1 * m2) / r^2
where: F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
If the distance between the two objects decreases to 1/2 of its original distance, then the new force of gravity (F') is given by:
F' = G * (m1 * m2) / (r/2)^2 = G * (m1 * m2) / (r^2 / 4) = 4 * G * (m1 * m2) / r^2 = 4F
So, the gravitational force between the two objects will increase by 4x its original value.
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