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  • In a certain region of space gravitational field is given by <img alt="\mathrm{ I=-\left(\frac{k}{r}\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20I%3D-%5Cleft%28%5Cf

In a certain region of space gravitational field is given by \mathrm{ I=-\left(\frac{k}{r}\right)}. Taking the reference point to be at \mathrm{r=r_0 \: with \: v=v_0,} the potential \mathrm{ (V)} is given by
 

Option: 1

\mathrm{V=K \log \frac{\mathrm{r}}{\mathrm{r}_0}+\mathrm{V}_{\mathrm{o}}}


 


Option: 2

\mathrm{\quad V=K \log \frac{r}{r_0}-v_0}
 


Option: 3

\mathrm{V=K \log \frac{r_0}{r}+v_0}
 


Option: 4

\mathrm{\quad V=K \log \frac{r_0}{r}-V_o}


Answers (1)

best_answer

We know that \mathrm{I}=-\frac{\mathrm{dv}}{\mathrm{dr}}

\mathrm{ \Rightarrow-\frac{\mathrm{k}}{\mathrm{r}}=-\frac{\mathrm{dV}}{\mathrm{dr}} \Rightarrow \int_{\mathrm{Vo}}^{\mathrm{V}} \mathrm{dv}=\mathrm{K}\mathrm{ \int_{\mathrm{r}_{\mathrm{o}}}^{\mathrm{r}} \frac{\mathrm{dr}}{\mathrm{r}} }}

\mathrm{ \Rightarrow \mathrm{V}=\mathrm{K} \log \frac{\mathrm{r}}{\mathrm{r}_{\mathrm{o}}}+\mathrm{v}_{\mathrm{o}}}

Hence option 3 is correct.

 



 

Posted by

avinash.dongre

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