A) \[G{{\pi }^{2}}{{R}^{2}}\]
B) \[\frac{128}{81}G{{\pi }^{2}}{{R}^{4}}{{\rho }^{2}}\]
C) \[\frac{128}{81}G{{\pi }^{2}}\]
D) \[\frac{128}{81}{{\pi }^{2}}{{R}^{4}}G\]
Correct Answer: B
Solution :
[b]\[{{\operatorname{m}}_{1}} =\frac{4}{3}\pi {{R}^{3}}\rho , {{m}_{2}} =\frac{4}{3}\pi {{\left( 2R \right)}^{3}}\rho \], distance between the centres of the two spherical objects, \[r=3R.\] \[F=\frac{G{{M}_{1}}{{m}_{2}}}{{{r}^{2}}}\] \[=G\left( \frac{4}{3}\pi {{R}^{3}}\rho \right)\left( 8\times \frac{4}{3}\pi {{R}^{3}}\rho \right)\times \frac{1}{{{\left( 3R \right)}^{2}}}\] \[=\frac{128}{81}G{{\pi }^{2}}{{R}^{4}}{{\rho }^{2}}\]
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