Two identical copper spheres of radius R are in contact with each other. If the gravitational attraction between them is F, find the relation between F and R.

Options

A. `F prop R^4`
B. `F prop R^(3//2)`
C. `F prop R^(-2)`
D. `F prop R^(-4)`

Answer

A

Explanation

Let M be the mass of each copper sphere and p be the uniform density of copper.
`:. M =(4/3 piR^3)rho`
The force of gravitational attraction between the two spheres is
`F=(GM M)/((R+R)^2)=G/(4R^2)(4/3piR^2rho)^2=(4/9Gpi^2rho^2)R^4`
If p is constant, then `F prop R^4`