The gravitational force between two objects is 10 N. If the distance between the

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Question: The gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

Options:

Correct Answer: 40 N

Solution:

If the distance is halved, the gravitational force increases by a factor of 4, so the new force is 40 N.

The gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

The gravitational force between two objects is 10 N. If the distance between them is halved, what will be the new force?

Step 1: Understand that gravitational force depends on the distance between two objects.
Step 2: Recall the formula for gravitational force: F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
Step 3: Note that if the distance (r) is halved, 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 the equation: (r/2)^2 = r^2 / 4, so F' = G * (m1 * m2) / (r^2 / 4) = 4 * (G * (m1 * m2) / r^2).
Step 6: This shows that the new force (F') is 4 times the original force (F).
Step 7: Since the original force is 10 N, multiply it by 4: 10 N * 4 = 40 N.
Step 8: Conclude that the new gravitational force is 40 N.

Gravitational Force – The gravitational force between two objects is inversely proportional to the square of the distance between them, as described by Newton's law of universal gravitation.
Inverse Square Law – When the distance between two masses is halved, the gravitational force increases by a factor of four (2^2).