Neet Solved Paper 2013 Question 11
Question: Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2 m, 4 m, 8 m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be
Options:
A) $ -G $
B) $ -\frac{8}{3}G $
C) $ -\frac{4}{3}G $
D) $ -4G $
Show Answer
Answer:
Correct Answer: D
Solution:
- The resulting gravitational potential, $ V=-2G[ \frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+… ] $
$ \Rightarrow $ $ V=-2G[ 1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}… ] $
$ \Rightarrow $ $ V=-2G{{( 1+\frac{1}{2} )}^{-1}} $
$ \Rightarrow $ $ V=-\frac{2G}{( 1-\frac{1}{2} )}=-\frac{2G}{( \frac{1}{2} )}=-4G $
