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How Gravitational Potential due to uniform solid sphere of radius R varies with the distance r from its center (For r< R) ??

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A Avinash Dongre

As shown in the below figure

If Gravitational Potential due to uniform solid sphere= V

Then For Inside surface I.e for $r<R$

$V=-\frac{GM}{2R}\left[3-\left ( \frac{r}{R} \right )^{2}\right]$

$R\rightarrow$ Radius of shell

$r\rightarrow$ Position of Pt.

$M\rightarrow$ Mass of Solid sphere

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