The distance of the centres of moon and ea

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The distance of the centres of moon and earth is $D$. The mass of earth is $81$ times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero

A

$\frac{D}{2}$

B

$\frac{{2D}}{3}$

C

$\frac{{4D}}{3}$

D

$\frac{{9D}}{{10}}$

The distance of the centres of moon and earth is $D$. The mass of earth is $81$ times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero

Force will be zero at the point of zero intensity

$x = \frac{{\sqrt {{m_1}} }}{{\sqrt {{m_1}} + \sqrt {{m_2}} }}d$

$ = \frac{{\sqrt {81M} }}{{\sqrt {81M} + \sqrt M }}D = \frac{9}{{10}}D.$