If two objects are placed in space, how does the gravitational force between the

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Question: If two objects are placed in space, how does the gravitational force between them change if the distance is halved?

Options:

Correct Answer: It becomes four times stronger

Solution:

If the distance is halved, the gravitational force increases by a factor of four, as it is inversely proportional to the square of the distance.

If two objects are placed in space, how does the gravitational force between them change if the distance is halved?

If two objects are placed in space, how does the gravitational force between them change if the distance is halved?

Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Know that the formula for gravitational force (F) is F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
Step 3: If the distance (r) is halved, it means we replace r with r/2 in the formula.
Step 4: Substitute r/2 into the formula: F = G * (m1 * m2) / (r/2)^2.
Step 5: Simplify (r/2)^2 to get (r^2 / 4). So, the formula becomes F = G * (m1 * m2) / (r^2 / 4).
Step 6: When you divide by (r^2 / 4), it is the same as multiplying by 4. So, F = 4 * (G * (m1 * m2) / r^2).
Step 7: This shows that the gravitational force increases by a factor of 4 when the distance is halved.

Gravitational Force – The gravitational force between two objects is determined by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance between the centers of the two objects.
Inverse Square Law – This law indicates that if the distance between two masses is halved, the gravitational force increases by the square of the factor of change in distance.