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7.Gravitation
normal
If the distance between centres of earth and moon is $D$ and the mass of earth is $81\, times$ the mass of moon, then at what distance from centre of earth the gravitational force will be zero
A
$\frac{D}{2}$
B
$\frac{{2D}}{3}$
C
$\frac{{4D}}{3}$
D
$\frac{{9D}}{10}$
Solution
$\frac{\mathrm{GMe}}{\mathrm{r}^{2}}=\frac{\mathrm{GMm}}{(\mathrm{D}-\mathrm{r})^{2}}$
$\frac{81 \mathrm{Mm}}{\mathrm{r}^{2}}=\frac{\mathrm{Mm}}{(\mathrm{D}-\mathrm{r})}$
$\frac{9}{r}=\frac{1}{D-r} \Rightarrow r=\frac{9}{10} D$
Standard 11
Physics
