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  • In a certain region of space, the gravitational field is given by  <img alt="I=-\left ( \frac{K}{R} \right )." src="https://entrancecorner.oncodecogs.com/gif.latex?I%3D-%5Cleft%20%28%20%5Cfrac

In a certain region of space, the gravitational field is given by  I=-\left ( \frac{K}{R} \right ).Taking the reference point to be at r=r_{0} and potential at the reference point as   V = V _{0}.

Then find the potential at a general point ?

Option: 1

Klog(\frac{r}{r_{0}})+V_{0}

 


Option: 2

  Klog(\frac{r_{0}}{r})+V_{0}

 

 

 


Option: 3

Klog(\frac{r}{r_{0}})-V_{0}

 


Option: 4

Klog(\frac{r_{0}}{r})-V_{0}

 


Answers (1)

best_answer

 As I=\frac{-dv}{dr} or dv=-Idr

\int _{v_{0}}^{v}dv=-\int _{r_{0}}^{r}\left ( \frac{-k}{r} \right )dr

\left [ V \right ]_{vo}^{v}=K\left [ log r\right ]_{ro}^{r}=K\left [ logr-logr_o \right ]

V-V_{0}= K log\frac{r}{r_{o}}\Rightarrow V=K log\frac{r}{r_{0}}+V_{o}

 

Posted by

Sanket Gandhi

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