Four particles of masses m, 2m, 3m, 4m are kept in sequence at the corners of side 'a'. The magnitude of gravitational force on a particle of mass 'm' placed at the center of the square will be.
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Answer:
a = length of each side of square
r = distance of each corner from center =
(
2)
a
F₁ = force by mass "m"=Gm²/r²=2Gm²/a²
F₂ = force by mass "2m" =2Gm²/r²=4Gm²/a²
F₃ = force by mass "3m"=3Gm²/r²=6Gm²/a²
F₄ = force by mass "4m" =4Gm²/r²=8Gm²/a²
F₁₃ = net force of F₁ and F₃=F₃−F₁=(6Gm²/a²)−(2Gm²/a²)=4Gm²/a²
F₂₄ = net force of F₂ and F₄=F₄−F₂=(8Gm²/a²)−(4Gm²/a²)=4Gm²/a²
magnitude of net force using pythagorean theorem is given as
F=
(F²₁₃+F²₂₄)
=
((4Gm²/a²)²+(4Gm²/a²)²)
=(5.66)Gm²/a²
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