CBSE-XI-Physics
11: Gravitation
- #8Suppose the gravitational potential due to a small system is k/r2 at a distance r from it. What will be the gravitational field? Can you think of any such system? What happens if there were negative masses?Ans : The gravitational potential due to the system is given as `` V=\frac{k}{{r}^{2}}``.
Gravitational field due to the system:
`` E=-\frac{dV}{dr}``
`` \Rightarrow E=-\frac{d}{dr}\left(\frac{k}{{r}^{2}}\right)=-\left(-\frac{2k}{{r}^{3}}\right)``
`` \Rightarrow E=\frac{2k}{{r}^{3}}``
We can see that for this system, `` E\propto \frac{1}{{r}^{3}}``
This type of system is not possible because `` {\text{F}}_{g}`` is always proportional to inverse of square of distance(experimental fact).
If there were negative masses, then this type of system is possible.
This system is a dipole of two masses, i.e., two masses, one positive and the other negative, separated by a small distance.
In this case, the gradational field due to the dipole is proportional to `` \frac{1}{{r}^{3}}``.
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