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) \[\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{\sqrt{2}}a\]
Correct Answer: C
Solution :
[c] \[W=m\left( {{V}_{2}}-{{V}_{1}} \right)\] when, \[{{V}_{1}}=-\left[ \frac{G{{M}_{1}}}{a}+\frac{G{{M}_{2}}}{\sqrt{2}a} \right],\] \[{{V}_{2}}=-\left[ \frac{G{{M}_{2}}}{a}+\frac{G{{M}_{1}}}{\sqrt{2}a} \right]\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,W=\frac{Gm\left( {{M}_{2}}-{{M}_{1}} \right)}{a\sqrt{2}}(\sqrt{2}-1)\]
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