Two particles of masses `m_(1)` are`m_(2)` placed along the x and y axes respectively at a distance from the origin. Calculate the gravitational field at a point P shown in figure below.

Explanation

Gravitational field due to `m_(1)` at a point .P. is given by
`vec(E) _(1) = - (Gm_(1))/(a^(2)) hat(j)`
Gravitational field due to `m_(2)` at a point .P. is given by
` vec(E)_(2) = - (Gm_(2))/(a^(2))hat(j)`
`vec(E)_("total") = - (Gm_(1))/(a^(2)) hat(j) = (Gm_(2))/(a^2)hat(i)`
` = G/a^(2) (m_(1)hat(j)+m_(2)hati)`
The direction of the total gravitational field is determined by the relative value of `m_(1)and m_(2)`
When , `m_(1) =m_(2) =m`
`vec(E)_("total") = - (Gm)/(a^(2)) (hat(i)+hat(j))`
(`hat(i)+hat(j) =hat(j)+hat(i)` as vectors obeys communtation law )
`vec(E )_("total")` points towards the origin of the co - ordinate system and the magnitude of gravitational field is , `vec(E )_("total") = sqrt(2) (Gm)/(a^(2))`