Two masses of `500 kg` each are placed at two points `A` and `B`, distance `5 m` apart. There is a point `P` such that `AP = 3 m` and `BP = 4 m`. Find (i) the magnitude of gravitational intensity at `P` and
(ii) gravitational potential at `P`.
Given `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

Explanation

Refer to Fig.
`5^(2) = 3^(2) + 4^(2)` or `AB^(2) = (AP)^(2) + (BP)^(2)`
So `/_APB = 90^(@)`

(i) Gravitational intensity at `P` due to mass at `A` is
`I_(1) = (G xx 500)/((3)^(2)) = (500)/(9) G along PA`
Gravitational intensity at `P` due to mass at `B` is
`I_(2) = (G xx 500)/((4)^(2)) = (500)/(16) G along PB`
As `/_APB = 90^(@)`, so the resultant gravitational intensity (in magnitude) at `P` is
`I = sqrt(I_(1)^(2) + I_(2)^(2)) = sqrt(((500)/(9)G)^(2) + ((500G)/(16))^(2))`
`=- (6.67 xx 10^(-11) xx 500 xx 7)/(12)`
`= - 1.945 xx 10^(-8) J kg^(-1)`