Compare the gravitational force on a body of mass 1 kg due to the earth with the force on the same body due to another body of mass 1 kg at a distance of 1 m from the first body. (Mass of the earth `=6xx10^(23)kg`, radius of the earth = 6400 km)

Explanation

In the first case, `m_(1)=1kg`
`m_(2)=6xx10^(24)kg and r=6400km=6.4xx10^(6)m`
Gravitational force on the body,
`F_(1)=(Gm_(1)m_(2))/(r^(2))=(Gxx1kgxx6xx10^(24)kg)/((6.4xx10^(6)m)^(2))`
`=(Gxx6xx10^(24)kg^(2))/((6.4)^(2)xx10^(12)m^(2))`
In the second case, `m_(1)=1kg`
`m_(2)=1kg and r =1 m`.
Gravitational force on the body.
`F_(2)=(Gm_(1)m_(2))/(r^(2))=(Gxx1kgxx1kg)/((1m)^(2))`
`therefore (F_(1))/(F_(2))=(6xx10^(24))/((6.4)^(2)xx10^(12))=1.465xx10^(11)" OR"`
`(F_(2))/(F_(1))=6.826xx10^(-12)`.
Thus, `F_(2) lt lt F_(1)`.