Gravitation Question 367
Question: Two rings each of radius ‘a’ are coaxial and the distance between their centres is a. The masses of the rings are$ [M_{1}andM_{2}] $ . The work done in transporting a particle of a small mass m from centre $ [{C_{1}} to C_{2}] $ is :
Options:
A) $ [\frac{Gm\left( M_{2}-M_{1} \right)}{a}] $
B)$ [\frac{Gm\left( M_{2}-M_{1} \right)}{a\sqrt{2}}\left( \sqrt{2}+1 \right)] $
C) $ [\frac{Gm\left( M_{2}-M_{1} \right)}{a\sqrt{2}}\left( \sqrt{2}-1 \right)] $
D) $ [\frac{Gm\left( M_{2}-M_{1} \right)}{\sqrt{2}}a] $
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Answer:
Correct Answer: C
Solution:
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$ [W=m\left( V_{2}-V_{1} \right)] $
when,$ [V_{1}=-\left[ \frac{GM_{1}}{a}+\frac{GM_{2}}{\sqrt{2}a} \right],] $
$ [V_{2}=-\left[ \frac{GM_{2}}{a}+\frac{GM_{1}}{\sqrt{2}a} \right]] $ $ [\therefore ,,,,,,,,,,,,,,,,,,,,,,,,,,W=\frac{Gm\left( M_{2}-M_{1} \right)}{a\sqrt{2}}(\sqrt{2}-1)] $
