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Two bodies A and B having masses M and 3...

Two bodies A and B having masses M and 3M respectively are kept at a distance 2.73 m apart. A small particle of mass m is to be place so that the net gravitational force on it, due to A and B is zero. What will be its distance from body A ?

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Now, `|vec(F)_(CA)| = |vec(F)_(CA)|`
` :. (GMm)/(x^(2)) = (G3Mm)/((y-x)^(2))`
` :. 1/(x^(2)) = 3/((y-x)^(2))`
` :. y - x = sqrt(3)x`
` :. y = (sqrt(3)+1)x `
` :. x = y/(sqrt(3)+1)`
` = y/(1.732 +1)`
` :. " "x= y/(2.732 )`
` = (2.73)/(2.732 ) = 1m `
` :. ` A particle of mass m should be placed at 1 m apart from body A .
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