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 of the 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) = 250 kg , r = 30 cm = 0.30 m`,
`F = 0.40 mg wt = 0.40 xx 10^(-6) kg wt`
`= 0.40 xx 10^(-6) xx 9.8 N`
`F= (Gm_(1)m_(2))/(r^(2))` or `G = (F r^(2))/(m_(1) m_(2))`
But `g = (GM_(e))/(R_(e)^(2))` or `M_(e) = (g R_(e)^(2))/(G) = (g R_(e)^(2))/(F r^(2)) m_(1) m_(2)`
`= (9.8 xx (6 xx 10^(6))^(2) xx 20 xx 250)/((0.40 xx 10^(-6) xx 9.8) xx (0.3)^(2)) = 5 xx 10^(24) kg`