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Question
Calculate the gravitational field at point O due to three masses m1, m2 and m3 whose positions are given by the following figure. If the masses m1 and m2 are equal what is the change in a gravitational field at the point O?
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Solution
Gravitational field due to 'm1' at a point 'O' is `vec"E"_1 = "Gm"_1/"a"^2 hat"i"`
A negative sign indicates field acting along the negative x-direction
Gravitational field due to 'm2' at a point 'O' is `vec"E"_2 = -"Gm"_2/"a"^2 hat"i"`
Gravitational field due to 'm3' at a point 'O' is `vec"E"_3 = "Gm"_3/"a"^2 hat"j"`
`vec"E" = vec"E"_1 + vec"E"_2 + vec"E"_3`
= `"Gm"_1/"a"^2 hat"i" - "Gm"_2/"a"^2 hat"i" + "Gm"_3/"a"^2 hat"j"`
`vec"E" = "G"/"a"^2 [("m"_1 - "m"_2)hat"i" + "m"_3hat"j"]`
If the masses m1 = m2, then
`vec"E" = "G"/"a"^2 ["m"_3hat"j"]`
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