A spherical mass of `20 kg` lying on the surface of the Earth is attracted by another spherical mass of `150 kg` with a force equal to `0.23 mg f`. The centres o fthe two masses are `30 cm` apart. Calculate the mass of the Earth. Radius of the Earth is `6 xx 10^(6)m`.

Explanation

Here, `m_(1) = 20 kg , m_(2) = 150 kg`,
`r = 30 cm = 0.30 m`
`F = 0.23 mg f = 0.23 xx 10^(-6) kg f`
`= 0.23 xx 10^(-6) xx 9.8 N`
`F = (Gm_(1)m_(2))/(r^(2))`
or `G = (F r^(2))/(m_(1)m_(2)) = ((0.23 xx 10^(-6) xx 9.8) xx (0.30)^(2))/(20 xx 150)`
`= 6.762 xx 10^(-11) Nm^(2) kg^(-2)`
Mass of earth, `M = (gR^(2))/(G) = (9.8 xx (6 xx 10^(6))^(2))/(6.762 xx 10^(-11))`
`= 5.2 xx 10^(24) kg`