8.21 Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the midpoint of the line joining the centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

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Vishal Baghel | Contributor-Level 10

4 months ago

Mass of each sphere, M = 100 kg

Separation between the spheres, r = 1 m

X is the midpoint between the spheres.

Gravitational force at point x will be zero. This is because gravitational force exerted by each spheres will act in opposite directions.

Gravitational potential at point x:

= $\frac{- G M}{\frac{r}{2}}$ $\frac{- G M}{\frac{r}{2}}$ = $-$ 4 $\frac{G M}{r}$ = $- \frac{4 * 6.67 * 10^{- 11} * 100}{1}$ = $- 2.668 * 10^{- 8}$ J/kg

Any object placed at point x will be in equilibrium state, but the equilibrium is unstable. This is because any change in the position of the object will change the effective force in that direction.

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