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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.

Text Solution

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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 mid-point
`F_(1) = F_(2) = (GMm)/((5R)^(2))`
The direction of forces are opposite, therefore not force acting on the object is zero. To check the stability of the equilibrium, we displace the object through a small distance `x` towards sphere A
Now, force acting towards sphere A, `F'_(1) = (GMm)/((5R - x)^(2))`
Force acting towards sphere B, `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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