Question

If the mass of moon is $\frac{M}{81}$ , where M is the mass of earth, find the distance of the point, where gravitational field due to earth and moon cancel each other, from the centre of moon. Given that distance between centres of earth and moon is 60 R, where R is the radius of earth.

Moderate

Solution

Equating gravitational field intensities, $\frac{\frac{G M}{81}}{r^{2}} = \frac{G M}{(60 R - r)^{2}}$
Solving above equation, we get
$60 R - r = 9 r \Rightarrow r = 6 R$

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