Question

Objects 1 and 2 attract each other with a gravitational force of 72.0 units. If the mass of Object 1 is one-fourth the original value AND the mass of object 2 is tripled AND the distance separating Objects 1 and 2 is halved, then the new gravitational force will be _____ units.

Answer 1

Answer:

New gravitational force, F' = 216 units

Explanation:

Given that,

Gravitational force between object 1 and 2, F = 72 N

The gravitational force between two objects is given by :

$F=\dfrac{Gm_1m_2}{r^2}$

$\dfrac{Gm_1m_2}{r^2}=72$............(1)

If the mass of object 1, $m_1'=\dfrac{m_1}{4}$

$m_2'=3m_2$

If the distance between objects is halved, $r'=\dfrac{r}{2}$

Let new gravitational force is F'. It is changed to :

$F=\dfrac{Gm'_1m'_2}{r'^2}$

$F'=\dfrac{G\times \dfrac{m_1}{4}\times 3m_2}{(\dfrac{r}{2})^2}$

$F'=3\times \dfrac{Gm_1m_2}{r^2}$

$F'=3\times F$

$F'=3\times 72$

F' = 216 units

So, the  new gravitational force will be 216 units.