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Gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsGravitation3 Marks
Question
Two heavy spheres each of mass $100kg$ and radius $0.10m$ are placed $1.0m$ 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?
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Answer

Gravitational field at the mid-point of the line joining the centres of the two spheres $=\mathrm{GM} /(\mathrm{r} / 2)^2$ (along negative r ) $+\mathrm{GM} /(\mathrm{r} / 2$ ) (along r ) $=0$ Gravitational potential at the midpoint f the line joining the centres of the two spheres is V $=-\mathrm{GM} / \mathrm{r} / 2+(-\mathrm{GM} / \mathrm{r} / 2)=-4 \mathrm{GM} / \mathrm{r}=-4 \times 6.67 \times 10^{-11} \times 100 / 1.0=-2.7 \times 10^{-8} \mathrm{~J} / \mathrm{Kg}$ As the effective force on the body placed at mid-point is zero, sso the body is in equilibrium. If the body is displaced a little towards either mass body from its equilibrium position, it will not return back to its inital position of equilibrium. Hence, the body is in unstable equilibrium.

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