If the distance from a mass is doubled, how does the gravitational field strengt

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Question: If the distance from a mass is doubled, how does the gravitational field strength change?

Options:

Correct Answer: It becomes one-fourth.

Solution:

The gravitational field strength is inversely proportional to the square of the distance, so it becomes one-fourth.

If the distance from a mass is doubled, how does the gravitational field strength change?

If the distance from a mass is doubled, how does the gravitational field strength change?

Step 1: Understand that gravitational field strength (g) depends on the distance (r) from the mass.
Step 2: Remember the formula for gravitational field strength: g = G * (M / r^2), where G is the gravitational constant and M is the mass.
Step 3: Note that 'r' is the distance from the mass.
Step 4: If the distance (r) is doubled, it becomes 2r.
Step 5: Substitute 2r into the formula: g = G * (M / (2r)^2).
Step 6: Calculate (2r)^2, which is 4r^2.
Step 7: Now the formula looks like this: g = G * (M / 4r^2).
Step 8: This shows that the new gravitational field strength is one-fourth of the original strength because of the 4 in the denominator.

Gravitational Field Strength – The gravitational field strength (g) is defined as the force per unit mass experienced by a small test mass placed in the field, and it is inversely proportional to the square of the distance (r) from the mass creating the field.
Inverse Square Law – This law states that the strength of a physical quantity (like gravitational field strength) decreases with the square of the distance from the source.