Question

When the distance between two stars decreases by one-third, the force between them ___

Answer 1

the force increases by 9/4

Step-by-step explanation:

The gravitational force between two stars is given by:

`F=G(m_1 m_2)/(r^2)`

where

G is the gravitational constant

m1 and m2 are the masses of the two stars

r is the separation between the two stars

In this problem, the distance between the two stars is decreased by 1/3, which means that the new distance is

`r'=r-(1)/(3)r=(2)/(3)r`

So, the new gravitational force will be

`F'=G(m_1 m_2)/((2/3)^2)=G(m_1 m_2)/((4)/(9)r^2)=(9)/(4)F`