A) 2
B) 6
C) \[{{10}^{-2}}\]
D) 0.6
Correct Answer: C
Solution :
\[\Delta {{F}_{1}}={{F}_{1}}-{{F}_{2}}\] \[\Delta {{F}_{2}}={{F}_{1}}^{'}-{{F}_{2}}^{'}\] \[\Delta {{F}_{1}}=\frac{G{{m}_{m}}{{m}_{e}}}{(0.4\times {{10}^{6}}-\operatorname{Re})}-\frac{G{{m}_{m}}{{m}_{e}}}{(0.4\times {{10}^{6}}+\operatorname{Re})}\] \[\Delta {{F}_{2}}=\frac{G{{m}_{m}}{{m}_{s}}}{(150\times {{10}^{6}}-\operatorname{Re})}-\frac{Gm{{e}_{m}}{{m}_{e}}}{(150\times {{10}^{6}}+\operatorname{Re})}\] \[\frac{\Delta {{F}_{1}}}{{{F}_{2}}}=\frac{G{{M}_{m}}Me\left\{ \frac{1}{0.4\times {{10}^{6}}-\operatorname{Re}}-\frac{1}{0.4\times {{10}^{6}}+\operatorname{Re}} \right\}}{G{{M}_{e}}Ms\left\{ \frac{1}{150\times {{10}^{6}}-\operatorname{Re}}-\frac{1}{150\times {{10}^{6}}+\operatorname{Re}} \right\}}\] \[=\frac{\frac{Mm}{Ms}\left\{ \frac{0.4\times {{10}^{6}}+\operatorname{Re}-0.4\times {{10}^{6}}+\operatorname{Re}}{(0.4\times {{10}^{6}}-\operatorname{Re})(0.4\times {{10}^{6}}+\operatorname{Re})} \right\}}{\left\{ \frac{150\times {{10}^{6}}+\operatorname{Re}-150\times {{10}^{6}}+\operatorname{Re}}{(150\times {{10}^{6}}-\operatorname{Re})(150\times {{10}^{6}}+\operatorname{Re}} \right\}}\] \[\frac{Mm}{Ms}\times \frac{(150\times {{10}^{6}}-\operatorname{Re})(150\times {{10}^{6}}+\operatorname{Re})}{(0.4\times {{10}^{6}}-\operatorname{Re})(0.4\times {{10}^{6}}+\operatorname{Re}}=\frac{(150-.0064)(150+.0064)}{(0.4-.0064)(0.4+.0064)}\] \[=\frac{Mm}{Ms}\frac{149.99\times 150.0064}{0.3936\times .4064}\] \[=140657.633\times \frac{8\times {{10}^{22}}}{2\times {{10}^{30}}}\] \[\approx 0.0056\] \[\approx 0.01\] \[\approx {{10}^{-2}}\]
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