Consider two solid uniform spherical objects of the same density `rho`. One has radius `R` and the other has radius `2R`. They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?

Options

A. `Gpi^(2)R^(4)`
B. `128/81Gpi^(2)R^(4)rho^(2)`
C. `128/81Gpi^(2)`
D. `128/87pi^(2)R^(2)G`

Answer

B

Explanation

`m_(1)=4/3piR^(3)rho, m_(2)=4/2pi(2R)^(3)rho`, distance between the centres of the two spherical objects `r=3R`
`F=(GM_(1)m_(2))/(r_(2))=G(4/3piR^(3)rho)(8xx4/3piR^(2)rho)x1/((3R)^(2))`
`=128/81Gpi^(2)R^(4)rho^(2)`