The sun's mass is about 3.2 x 105 times the earth's mass. The sun is about 400 times as far from the earth as the earth is from the moon. Assume that the sun-moon distance is constant and equal to sun-earth distance. The ratio of the magnitudes of the gravitational pull of the sun on the moon Fms and of the earth on the moon Fem will be FmsFme='n'. The value of n is ____________
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answer is 2.
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Detailed Solution
Let m = moon's mass, Ms = sun's massMe = earth's massrms = the centre-to-centre distance from the sun to the moonrme = the centre-to-centre distance from the earth to the moonFms = gravitational force exerted on the moon by the sunFme = gravitational force exerted on the moon by the earthThen FmsFme=MSrme2Merms2Putting the values FmsFme=MSMermerms2 =3.2×10514002=3216=2