Question

Two bodies having masses, 'M' and 'm' respectively, when separated by a distance 'd'

exert a force 'F' on each other. What happens when:

I. The mass of one of the objects is doubled.

II. The distance between the two bodies is reduced to half.

Also, write the steps used to calculate your answer.​

Answer 1

$\bigstar$ EXPLAINATION $\bigstar$

• Given

There are two bodies of mass m and M respectively and they are separated by a distance d and they exert a gravitational force F on each other

• To find

What happens to the gravitational force between them

i) When their one of their mass is doubled ????

ii) The distance between the two bodies is reduced to half

• Procedure

We know that,

$F = \frac{G\times m\times M}{d²}$

Let the gravitational force between them when one of their mass is doubled be F'

Let the body of mass m's mass have been doubled

$F'= \frac{G\times 2m\times M}{d²}$

$F' = 2\times \frac{G\times m\times M}{d²}$

$F' = 2F$

Let the gravitational force between them when the distance between them is havled be f

$f = \frac{G\times m\times M}{ (\frac{d}{2})^2 }$

$f = \frac{G\times m\times M}{ (\frac{d²}{4}) }$

$f = 4\times \frac{G\times m\times M}{d²}$

$f = 4F$