Question

13. If the distance between two bodies is increased
two times, then how many times, the mass of one
of the bodies needs to be changed to maintain the
same gravitational force?


PLEASE ANSWER CORRECTLY AND ONLY IF YOU ARE SURE ​

Answer 1

ANSWER:

• Mass is increased to 4 m.

GIVEN:

• The distance between two bodies is increased  two times.

TO FIND:

• How many times, the mass of one  of the bodies needs to be changed to maintain the  same gravitational force.

EXPLANATION:

$\boxed{\bold{\large{\gray{F=\dfrac{Gmm}{r^2}}}}}$

r = 2r

$\sf F'=\dfrac{Gmm}{(2r)^2}$

$\sf F'=\dfrac{Gmm}{4r^2}$

F/4 = F'

F = 4F'

Hence when F' is multiplied by 4 we get the the force F.

So one of the massess should be increased 4 times to make the force remain constant.

So one of the mass should be increased 4 times when distance is increased two times.

NEWTON's LAW OF GRAVAITATION:

Newton's law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their massess and inversely proportinal to the square of the distance between them.  

$\sf F\propto m_1m_2$

$\sf F\propto \dfrac{1}{r^2}$

$\sf F\propto \dfrac{m_1m_2}{r^2}$

$\boxed{\bold{\large{\gray{F=\dfrac{Gm_1m_2}{r^2}}}}}$

Here G is the constant of proportionality and is called Universal Gravitational Constant.