Two masses `800 kg `and `600 kg` are at a distance `25 cm` apart. Compute the magnitude of the intensity of the gravitational field at a point disatnce `20 cm` from the `800 kg` mass and `15 cm` frm the `600 kg` mass
`G = 6.66 xx 10^(-11) Nm^(2) kg^(-2)`.

Explanation

Let two masses `800 kg `and `600 kg` be at locations `A` and `B`, where distance `AB = 25 cm`.
Let `P` be a point, where `AP = 20 cm`
and `BP = 15 cm`.
Refer to Fig.
In `DeltaAPB, (AB)^(2) = 25^(2) = 625 sq. cm`
`(AP)^(2) + (PB)^(2) = (20)^(2) + (15)^(2) = 625 sq. cm`
`:. (AB)^(2) = (AP)^(2) + (PB)^(2)`,
so `/_APB = 90^(@)`
Gravitational intensity at `P` due to mass at `A`
`E_(A) = (GM)/(r^(2)) = G xx (800)/((0.20)^(2)) = 20,000 G` along `PA`
Graviational intensity at `P` due to mass at `B`
`E_(B) = (G xx 600)/((0.15)^(2)) = (80,000)/(3) G` along `PB`
Resulatnt gravitational intensity at `P` is
`:. E = sqrt(E_(A)^(2) + E_(B)^(2))`
`= sqrt((20,000G)^(2) + ((80,000 G)/(3))^(2))`
`= G xx (10,000)/(3) = (6.66 xx 10^(-11)) x (10,000)/(3)`
`= 2.22 xx 10^(-6) N`