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Question

The distance of a point from the earth's centre where the resultant gravitational field due to the earth and the moon is zero is...( The mass of the earth is 6.0× 1024 kg and that of the moon is 7.4× 1022 kg. The distance between the earth and the moon is 40 × 105 km.


A

1.6×105km

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B

3.6×105km

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C

4.6×105km

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D

6×105km

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Solution

The correct option is B

3.6×105km


The point must be on the line joining the centres of the earth and the moon and in between them. If the distance of the point from the earth is x, the distance from the moon is (4.0×105km - x). The magnitude of the gravitational field due to the earth is

E1=GMex2=G×6×1024kgx2

and magnitude of the gravitational field due to the moon is

E2=GMm(4.0×105kmx)2=G×7.4×1022kg(4.0×105kmx)2

These feild are in opposite directions. For the resultant field to be zero E1=E2

or, 6×1024kgx2 = 7.4×1022kg(4.0×105kmx2)2

or, x4.0×105kmx = (6×10247.4×1022)=9

or, x= 3.6 ×105 km


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