Question

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.

Answer 1

The gravitational force between them increases by a factor of 4

Step-by-step 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.