if the distance between two bodies is increased by 25% then % change in the gravitational force is
distance increased?
what is 1/1.25 ^2
To determine the percentage change in the gravitational force when the distance between two bodies is increased by 25%, we need to use the inverse square law of universal gravitation.
The formula for gravitational force is:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two bodies
G is the gravitational constant
m1 and m2 are the masses of the two bodies
r is the distance between the two bodies
If the distance between the two bodies is increased by 25%, it means the new distance (r') is 1.25 times the original distance (r):
r' = 1.25 * r
Now, let's calculate the new gravitational force (F') using the new distance (r'):
F' = G * (m1 * m2) / (r')^2
Substituting the expression for r':
F' = G * (m1 * m2) / (1.25 * r)^2
= G * (m1 * m2) / (1.5625 * r^2)
= (1/1.5625) * G * (m1 * m2) / r^2
= (0.64) * G * (m1 * m2) / r^2
Now, to find the percentage change in the gravitational force, we can calculate the difference between the new gravitational force (F') and the original gravitational force (F), and express it as a percentage of the original gravitational force:
% change in gravitational force = (F' - F) / F * 100
= ((0.64 * G * (m1 * m2) / r^2) - (G * (m1 * m2) / r^2)) / (G * (m1 * m2) / r^2) * 100
= (0.64 - 1) * 100
= -0.36 * 100
= -36%
Therefore, the percentage change in the gravitational force when the distance between two bodies is increased by 25% is -36%.