Assuming that the mass of the earth is 100 times larger than the mass of moon and the
radius of earth is about 4 times as that of moon, show that the weight of an object on
moon is 1/6th of that on earth.
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W ∝ M/R^2
W1 = weight of object on earth
W2 = weight of object on Moon
W1/W2 = (M1/M2) * (R2/R1)^2
W2 = W1 * (M2/M1) * (R1/R2)^2
= W1 * (M2 / (100M2)) * (4R2/R2)^2
= W1 * (1/100) * 16
≈ W1/6
W1 = weight of object on earth
W2 = weight of object on Moon
W1/W2 = (M1/M2) * (R2/R1)^2
W2 = W1 * (M2/M1) * (R1/R2)^2
= W1 * (M2 / (100M2)) * (4R2/R2)^2
= W1 * (1/100) * 16
≈ W1/6
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