Question

if the masses of two bodies are doubled , how should the distance between them be changed to keep the gravitational force constant ? please tell me fast its urgent

Answer 1

Given:

• Masses of bodies are doubled.

To find:

• How the distance has to be changed so that the gravitational force remains constant?

Calculation:

Let the force be F , mass of object be m and distance of separation be d.

$F =\dfrac{Gm^{2}}{d^{2}}$

Now, the masses have been doubled (i.e. 2m). Let the new distance of separation be x:

$\therefore F =\dfrac{G(2m)^{2}}{x^{2}}$

$\implies F =\dfrac{G(2m)^{2}}{x^{2}}$

$\implies \dfrac{Gm^{2}}{d^{2}}=\dfrac{G(2m)^{2}}{x^{2}}$

$\implies \dfrac{m^{2}}{d^{2}}=\dfrac{4m^{2}}{x^{2}}$

$\implies \dfrac{1}{d^{2}}=\dfrac{4}{x^{2}}$

$\implies x = 2d$

So, the new distance of separation is 2d (i.e. distance has to be doubled).