Question

If the distance between two bodies is increased by 25%,

then the % change in the gravitational force is : [1]

(a) Decreases by 36% (b) Increases by 36%

(c) Increases by 64% (d) Decreases by 64%?

Explain also ​

Answer 1

The answer is first one decreases by 36%.

Answer 2

Let us look at the answer:

Explanation:

The gravitational force is the force between two objects placed at a distance in nature.

F = G M m /r² where, g is Universal gravitational constant M, m are the masses of two objects and r is the distance between the two bodies.

As F ∝1/r , so by increasing the distance between the bodies, the force will decrease.

If we increase the distance, then r₁ = r + 25% of r = r + r/4 = 5r/4

So, new F₁ = G M m /r₁² = G M m / (5r/4)² = 16 G M m /25 r²

change = new F - inital F =  -9 G M m /25 r²

% decrease = 9 G M m /25 r² ÷  G M m /r² ×100 = 36%