If two objects are moved to a distance of half their original separation, how do

₹0.0

Question: If two objects are moved to a distance of half their original separation, how does the gravitational force change?

Options:

Correct Answer: It becomes four times stronger

Solution:

If the distance is halved, the force becomes 1/(1/2)^2 = 4 times stronger.

If two objects are moved to a distance of half their original separation, how does the gravitational force change?

If two objects are moved to a distance of half their original separation, how does the gravitational force change?

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: If the original distance (r) is halved, the new distance becomes r/2.
Step 4: Substitute the new distance 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).
Step 6: This can be rewritten as F' = G * (m1 * m2) * 4 / r^2, which shows that F' = 4 * F.
Step 7: Conclude that if the distance is halved, the gravitational force becomes 4 times stronger.

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 – This law states that if the distance between two masses is halved, the gravitational force increases by a factor of four (since (1/(1/2))^2 = 4).