Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change? Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change? The gravitational force decreases by a factor of 2. The gravitational force increases by a factor of 4. The gravitational force decreases by a factor of 4. The gravitational force remains unchanged. The gravitational force increases by a factor of 2.

Question

Physics

Sydney Ballard

29 January, 14:29

Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change? Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change? The gravitational force decreases by a factor of 2. The gravitational force increases by a factor of 4. The gravitational force decreases by a factor of 4. The gravitational force remains unchanged. The gravitational force increases by a factor of 2.

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Answers (1)

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Jennifer Bradford · Answer 1

The gravitational force between them increases by a factor of 4

Explanation:

Gravitational force is a force of attraction between two objects with masses M and m which are separated by a distance R. It is given mathematically as:

Fg = GMm/R²

Where G = Gravitational constant.

If the distance between their centers, R, decreases by a factor of 2, then it means the new distance between their centers is:

r = R/2

Hence, the gravitational force becomes:

Fg = GMm/r²

Fg = GMm / (R/2) ²

Fg = GMm / (R²/4)

Fg = 4GMm/R²

Hence, the gravitational force increases by a factor of 4.