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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. |
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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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