A) \[\frac{5}{6}\frac{GM}{{{x}^{2}}}\]
B) \[\frac{8}{9}\frac{GM}{{{x}^{2}}}\]
C) \[\frac{7}{8}\frac{GM}{{{x}^{2}}}\]
D) \[\frac{6}{7}\frac{GM}{{{x}^{2}}}\]
Correct Answer: D
Solution :
Mass of the small part \[=\frac{M}{\frac{4}{3}\pi {{R}^{3}}}\times \frac{4}{3}\pi {{\left( \frac{R}{2} \right)}^{3}}\] \[=\frac{M\times {{R}^{3}}}{{{R}^{3}}\times 8}\] \[M'=\frac{M}{8}\] g (rest part) = g (complete sphere) ? g (small part) \[=\frac{GM}{{{X}^{2}}}-\frac{G\frac{M}{8}}{{{\left( \frac{R}{2}+X \right)}^{2}}}\] From far point \[X>>\frac{R}{2}\] , so neglect \[\frac{R}{2}\] \[=\frac{GM}{{{X}^{2}}}\left( 1-\frac{1}{8} \right)\] \[=\frac{7\,GM}{8\,{{X}^{2}}}\]You need to login to perform this action.
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