Gravitation Question 342

Question: In a certain region of space, gravitational field is given by$ [I=-(K/r)] $ . Taking the reference point to be at $ [r=r_{0}] $ with $ [V=V_{0},] $ find the potential.

Options:

A) $ [K,\log \frac{r}{r_{0}}+V_{0}] $

B) $ [K,\log \frac{r_{0}}{r}+V_{0}] $

C) $ [K,\log \frac{r}{r_{0}}-V_{0}] $

D) $ [\log \frac{r_{0}}{r}-V_{0}r] $

Show Answer

Answer:

Correct Answer: A

Solution:

  • We know that intensity is negative gradient of potential, i.e.,

    $ [I=-(dV/dr)] $ and as here $ [I=-(K/r)] $ ,

    so $ [\frac{dV}{dr}=\frac{K}{r},i.e.,\int{dV=Ki}\int{\frac{dr}{r}}] $ or $ [V-V_{0}=K\log \frac{r}{r_{0}}] $ so $ [V=K\log \frac{r}{r_{0}}+V_{0}] $



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