Question

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

Answer 1

the force will increase by a factor 2.25

Step-by-step explanation:

The gravitational force between the two stars is given by:

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

where

G is the gravitational constant

m1, m2 are the masses of the two stars

r is the distance between the stars

If the distance is decreased by one-third, it means that the new distance is 2/3 of the previous distance

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

So the new force will be

`F'=G(m_1 m_2)/(((2)/(3)r)^2)=(9)/(4) G(m_1 m_2)/(r^2)=2.25 F`

So, the force will be 2.25 times the previous value.