1.

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 the weight of 0.25 mg. The centers of the two masses are 30 cm apart. Calculate the mass of earth. Radius of the earth = 6 X 10^6 m.

Answer»

We have m1= 20kg, m2= 250 kg, r = 0.3m, F = 0.25 mg wt = 0.25 x 10^-6kg wt.

F = 0.25 x 9.80 x 10^-6N

We have the formula F = G m1m2/ r^2

or G = F r^2/ m1m2

G = 0.25 x 9.80 x 10^-6x 0.30 x 0.30 / 20 x 250

= 0.2205 x 10^-6 / 5 x 10^3

G = 0.0441 x 10^-9

Now g = GM / R^2

g = g x R^2/ G

= 9.8 x (6 x 10^6)^2/ 0.0441 x 10^-9

= 8000 x 10^21

g = 8 x 10^24kg



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