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}] $
