Question

# Two point masses having mass m and 2m are placed at separation distance d. The point on the line joining point masses,where gravitational field intensity is zero will be at distance

A
2d3+1 from point mass "2m"
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B
2d31 from point mass "2m"
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C
d1+2 from point mass "m"
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D
d12 from point mass "m"
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Solution

## The correct option is C d1+√2 from point mass "m"Let r be the distance of the point from m where the gravitational field is zero. The field due to m will be cancelled by the field due to 2m. Hence, Em=E2m ⇒Gmr2=2Gm(d−r)2 ⇒1r=±√2d−r ⇒d−r=+√2r ⇒r(1+√2)=d ⇒r=d1+√2 Hence, option (c) is the correct answer. Key Concept: Between two masses, there will be a point where the gravitational field of one mass will be equal and opposite to the gravitational field of the other mass. Why this question: To make students familiar with the concept of gravitational field intensity.

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