Q: 8.21 Two heavy spheres each of mass  \small 100\hspace {1mm}kg and radius \small 0.10\hspace {1mm}m are placed \small 1.0\hspace {1mm}m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

Answers (1)

Gravitational force at the midpoint will be zero. This is because both spheres are identical and their forces will be equal but opposite in direction.

The gravitational potential is given by :

                                                  =\ \frac {-GM}{\frac{r}{2}}\ -\ \frac{-GM}{\frac{r}{2}}\ =\ \frac{-4GM}{r}

                                                                                                  =\ \frac{-4\times 6.67\times 10^{-11}\times 100}{1}

or                                                                                              =\ -2.67\times 10^{-8}\ J/Kg

At the midpoint, we have equal forces in the opposite direction so it is in equilibrium but if we move the body slightly then the particle will move in one direction (as one force will be greater). So it is an unstable equilibrium.

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