Suppose you and your friend have mass 50 kg each. Suppose also that you are standing such that your centres of gravity are 1m apart. Calculate the force of gravitation between you and your friend. Calculate also the force of gravity acting on you. [Mass of the earth `= 6 xx 10^(24) kg` , Radius of the earth `= 6.4 xx 10^(6)m`]
(Use `F = mg = G m M_(e)//R_(e)^(2)`)

Explanation

Mass of you and your friend = 50 kg each
Distance between you and your friend = 1m
Then,
Froce of gravitation `= F = (G m_(1)m_(2))/(r^(2))`
`= (6.673 xx 10^(-11) Nm^(-2) kg^(-2) xx 50 kg xx 50 kg)/(1m^(2)) = 1.67 xx 10^(-7) N`
Force of gravity acting on a body,
`F = mg = (Gm M_(e))/(R_(e)^(2))`
`M_(e)` is the mass of the earth
`R_(e)` is the radius of the earth
`6.673 xx 10^(-11) Nm^(-2) kg^(-2)`
`F = (xx50 kg xx 6 xx 10^(24) kg)/((6.4 xx 10^(6)m)^(2)) = (2001.9 xx 10^(13) Nm^(2))/(4.096 xx 10^(13) m^(2))`
`= 488.74 N`.