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Four particles of masses m, 2m, 3m and 4...

Four particles of masses m, 2m, 3m and 4m are kept in sequence at the corners of a square of side a. The magnitude of gravitation force acting on a particle of mass m placed at the centre of the square will be :

Text Solution

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The correct Answer is:
A, B, D
To calculate the gravitatioN/Al force on m due to other force

here `r=sqrt((a/2)^2+(a/2)^2)=a/sqrt2`
`vecF_(OB)=(G.m.2m)/r^2`
`vecF_(OC)=(G.m.3m)/r^2`
and `vecF_(OD)=(G.m.4m)/r^2`
Resultant force `=vecF_(OA)+vecF_(OB)+vecF_(OC)+vecF_(OD)`
`=(2Gmm)/a^2[-veci/sqrt2+vecj/sqrt2]+(4Gmm)/a^2[veci/sqrt2+vecj/sqrt/2]
`=(6Gmm)/a^2[veci/sqrt2-vecj/sqrt2]+(8Gmm)/a^2[(-veci)/sqrt2-(-vecj)/sqrt2]`
`F=(4sqrt2Gm^2)/a^2
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