How does the mass of the given object depend on the mass and radius of the earth? In an imaginary case, if the diameter of earth becomes half to the present diameter, and mass becomes four times to the present mass, then what will be the effect on the weight of the object ?

Answer

`W=M_e/R_e^2,` W='16W`

Explanation

The weight of an object on earth.s surface
`W=mg_(e)=m""(GM_(e))/(R_(c)^(2))`
`W alpha M_c/R_e^2`
In an imaginary case,
`Me^(.)=4M_e and R_e^(.)=R_e/2`
`W.=mg_c^.`
`=m ""(GM_(c)^(.))/(R_(e)^(2))`
`=mG ((4M_(e))/((Re)/(2))^(2))`
`=16 (m""(GM_(e)))/(R_(e)^(2))=16W`