A) \[mM=2\]
B) \[m=\frac{M}{2}\]
C) \[M={{m}^{2}}\]
D) none of these
Correct Answer: B
Solution :
\[F=G\frac{m(M-m)}{{{r}^{2}}}=km(M-m)\] where, \[k=\frac{G}{{{r}^{2}}}\] \[\therefore \] \[F=k\left[ \frac{{{M}^{2}}}{2}-\frac{{{M}^{2}}}{2}+mM-{{m}^{2}} \right]\] \[=k\left[ \frac{{{M}^{2}}}{4}-{{\left( \frac{M}{4}-m \right)}^{2}} \right]\] \[F\]is maximum, when\[\left( \frac{M}{4}-m \right)=0\] \[\Rightarrow \] \[m=\frac{M}{2}\]
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