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.

Two identical heavy spheres are separated by a distance 10 times their

1.	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.
Answer» <P> Solution :`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 midpointdue 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.