Question

If the distance between two bodies is increased by 25%, then the change in the gravitational forces
(a) Decreases by 36%
(b) Increases by 36%
(c) Increases by 64%
(d) Decreases by 64%

GIVE PROPER EXPLAINATION​

Answer 1

Answer:

Let suppose distance is 100m

F2/F1 = (r1/r2)^2

F2 = 16F1/25

%change - final - Initial/initial × 100

Answer - 36%

Decrease by 36%

F ~ 1/r^2

r increase than F decrease

Answer 2

Let us look at the Answer:

the force decreases by 36%.

Explanation:

We know that gravitational force is given by F = G Mm/r²

where F = gravitational force

          G = gravitational constant

          M, m = masses of the two bodies

           r = distance between two bodies.

So, by increasing the distance between the bodies the gravitational force will decrease as F ∝ 1/r

New radius = 25% of r + r = 5r/4

   F₁= new gravitational force

   F₁= G mM / (5r/4)² ⇒ F₁= 16/25 F ⇒ F₁= 64% F

change in gravitational force = final - inital  = 36% decrease.