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Explain briefly about the Gravitational potential

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Gravitational Potential-

In a gravitational field potential V at a point, P is defined as negative of work done per unit mass in changing the position of a test mass from some reference point to the given point.

Note-usually reference point is taken as infinity and potential at infinity is taken as Zero.

and it is given as

V=-\int \overrightarrow{I}\cdot \overrightarrow{dr}

where

V\rightarrow Gravitational potential

I\rightarrow Field Intensity

dr\rightarrow small distance

We can also write I=-\frac{dV}{dr}

This means a negative gradient of potential gives the intensity of the field.

The negative sign indicates that in the direction of intensity the potential decreases.

  • It is a scalar quantity.

  • Unit \to \; Joule/kg \; or \; m^{2}/sec^{2}

  • Dimension\: :\; \left [ M^{0}L^{2}T^{-2} \right ]

  • Gravitational Potential at a distance 'r'

If the field is produced by a point mass then 

I= \frac{GM}{r^{2}}

So V=-\int \overrightarrow{I}\cdot \overrightarrow{dr}

          V=-\frac{GM}{r}

                at r=\infty       V=0=V_{max}

Posted by

avinash.dongre

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