First slide

Gravitational field intensity

Question

Knowing that mass of moon is M/87, where M is the mass of tie earth, find the distance of the point from the moon, where gravitational field due to earth and moon cancel each other. Given that distance between earth and moon is 60 R, where R is the radius of earth

Moderate

A

8 R
B

4 R
C

6 R
D

2 R

Solution

Let x be the distance of the point from the moon where gravitational field intensity due to earth and moon cancel each other, Then
$\frac{G (M / 81)}{x^{2}} = \frac{GM}{(60 R - x)^{2}}$
or $\frac{1}{9 x} = \frac{1}{60 R - x}$
or $9 x = 60 R - x or 10 x = 60 R$
or $x = 6 R$

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