Spheres of the same material and same radius `r` are touching each other. Show that gravitational force between them is directly proportional to `r^(4)`.

Options

A. `r^2`
B. `r^3`
C. `r^4`
D. none of the above

Answer

C

Explanation

Two spheres are touching as shown below.

According to the question,
`m_(1)=m_(2)= "(volume)(density) = ((4)/(3)pir^(3))rho`
`:.` Gravitational force, `F=(Gm_(1)m_(2))/(r^(2))=(G((4)/(3)pir^(3))((4)/(3)pir^(3))rho^(2))/(r^(2))`
`rArr F prop r^(4)`.