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Two identical heavy spheres are separate...

 Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium ? Give reason for your answer.

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`implies` Let the mass and radius of each identical heavy sphere be M and R respectively. An object of mass m be placed at the mid-point P of the line joining their centres.

Force acting on the object placed at the midpoint due to each sphere `F_1 =F_2 =(GMm)/((5R)^2)` The direction of forces are opposite, therefore net force acting on the object is zero. This is equilibrium.
If we move object towards A by distance x,

`F._1=(GMm)/((5R-x)^2)`
`F._2=(GMm)/((5R+x)^2)`
As `F._1 gt F_2,` therefore a resultant force `(F_1 - F_2.)` acts on the object towards sphere A, therefore object start to move towards sphere A and hence equilibrium is unstable.
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