A) \[\frac{Gm({{m}_{1}}-{{m}_{2}})(\sqrt{2}-1)}{R\sqrt{2}}\]
B) \[\frac{Gm({{m}_{1}}-{{m}_{2}})}{R\sqrt{2}}\]
C) \[\frac{Gm({{m}_{2}}-{{m}_{1}})}{R\sqrt{2}}\]
D) \[\frac{Gm({{m}_{2}}-{{m}_{1}})}{R\sqrt{2}}\]
Correct Answer: A
Solution :
\[{{V}_{A}}=-\,\frac{G{{m}_{1}}}{R}-\,\frac{G{{m}_{2}}}{R\sqrt{2}}\] \[{{V}_{B}}=-\,\frac{G{{m}_{2}}}{R}-\frac{G{{m}_{1}}}{R\sqrt{2}}\] \[{{W}_{A-B}}=m({{V}_{B}}-{{V}_{A}})\] \[=\frac{gM({{m}_{1}}-{{m}_{2}})\,(\sqrt{2}-1)}{R\sqrt{2}}\]You need to login to perform this action.
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