Find the distance of a point from the earth's centre where the resultant gravitational field due to the earth and the moon is zero. The mass of the earth is `6.0xx10^24` kg and that of the moon is `7.4x10^22` kg. The distance between the earth and the moon is `4.0xx10^5km`.

Explanation

The point must be on the line joning the centres of the earth and the mon ad in between them. If the distance of the point from the earth is x, the distance form the moon is e(4.0xx10^5km-x)`. The magnitude o the gravittioN/A field due to the earth is
`E_1=(GM_e)/x^2=(Gxx6xx10^24kg)/x^2`
and magnitude of the gravitatioN/Asl field of the moon is
`E_2=(GM_m)/((4.0xx10^5km-x)^2)=(Gxx7.4xx10^22kg)/((4.0xx10^5km-x)^2)`
These fields are in opposite directions. For he resultnt field to be zero `E_1 =E_2`
`or (6xx10^24kg)/x^2=(7.4xx10^22kg)/((4.0xx10^5km-x)^2)`
or x/(4.0xx10^5km-x)=(sqrt(6xx10^24)/(7.4x10^22))=9
or `x=3.6xx10^5km`