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Question

# Compare the gravitational forces exerted by the Sun and the moon on the Earth. Which one exerts a greater force on the Earth? (Given: mass of the Sun, Ms=4×1031kg, mass of moon, Mm=6.3×1022kg, distance between the Sun and the Earth,rse=1.3×1012m and the distance between moon and the Earth, rme =4.5×108m.

A

Moon exerts a greater force and it is about 76 times the force due to the Sun

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B

Sun exerts a greater force and it is about 25 times the force due to moon

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C

Sun exerts a greater force and it is about 76 times the force due to the moon

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D

Both exert equal force on the Earth

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Solution

## The correct option is C Sun exerts a greater force and it is about 76 times the force due to the moon If mass of the Sun is Ms and mass of the Earth is Me and distance between the Sun and the Earth is rse, then force exerted by the Sun on the Earth is Fs=GMsMe(rse)2 ....................(1) Similarly, if mass of moon is Mm, mass of the Earth is Me, the distance between the moon and the Earth is rme, then force exerted by moon on the Earth is Fm=GMmMe(rme)2 .....(2) Dividing equation (1) by equation (2), we get: FsFm = GMsMe(rse)2 × (rme)2GMmMe = MsMm × (rme)2(rse)2 = 4×10316.3×1022 × (4.5×1081.3×1012)2 = 76.07 ∴The force exerted by the Sun on the Earth is about 76 times the force exerted by the moon on the Earth.

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