Question

Let us consider the force of gravitation between two objects at F and distance between them as r. What will be the effect on force if: a. r is reduced to 1/4th ? b. the masses of both the objects are increased by three times.

Answer 1

ATQ,
F = GMm ÷ (r)^2

a) r is 1/4
F' = GMm ÷ (r/4)^2
F' = GMm ÷ (r)^2/16
F' = 16GMm ÷ (r)^2
Hence New force will be 16 times more than the actual force.

b) Masses are 3 times

F" = G×3M×3m ÷ (r)^2
F" = 9GMm ÷ (r)^2

Hence new force is 9 times of actual force.

Answer 2

(a) Force will be increased 16 times.

(b) Force will be increased by 9 times.

Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

i.e: F = G $\frac{m1*m2}{r^2}$

where, m1 and m2 masses of the two objects and r is the distance between them.

Case (a):

Distance is quartered. R' = $\frac{r}{4}$

∴ F' = G $\frac{m1*m2}{r'^2}$

∴ F' = G  $\frac{m1*m2}{r'/4^2}$

∴ F' = G $\frac{m1*m2}{r'^2/16}$  

∴ F' = 16 F

Case (b):

Masses are increased three times. m'1 = 3m1 and m'2 = 3m2

F' = G $\frac{m'1*m'2}{r^2}$

∴ F' = G$\frac{3m1*3m2}{r^2}$

∴ F' = G  $\frac{9m1*m2}{r^2}$

∴ F' = 9F