Gravitation Question 366
Question: Infinite number of masses, each 1 kg are placed along the x-axis $ [at x=\pm1 m, \pm2m, \pm4m, \pm ] $ $ [8m, \pm 16M\ldots ] $ the magnitude of the resultant gravitational potential in terms of gravitational constant G at the or g in $ [(x=0)] $ is
Options:
A) G/2
B) G
C) 2G
D) 4G
Show Answer
Answer:
Correct Answer: C
Solution:
-
$ [V=\frac{GM}{r}=-G\left( \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+….\infty\right)] $
$ [=-G\left( \frac{1}{1-1/2} \right)=-2G] $
