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Two small bodies of masses 2.00 kg and 4...

Two small bodies of masses 2.00 kg and 4.00 kg are kept at rest at a separation of 2.0 m. Where should a particle of mass 0.10 kg be placed to experience no net gravitational force from these bodies? The particle is placed t this point.What is the gravitational potential energy of the system of three particle with usual reference level?

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The correct Answer is:
A, B, C, D
Let k0.1 kg mass is xm form 2 kg mass and `(2-x)m` from 4 kg mass.
`-.gt (2xx0.1)/x^2=-(4xx0.1)/((2-x^2)^2)`
or `0.2/x^2=0.4/((2-x^2)^2)`
or 1/x^2=2/((2-x^2)^2)`
or `(2-x)^2=2x^2`
`=(2-x)^2=2x^2`
`or 2-x=sqrt2 x`
`x(sqrt2+1)=2`
or` x=2/2.414`
`=0.83m from 2kg mass`.
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