Question

Four particles with mass m, 2m, 3m & 4m are placed at the four corners of a square of edge 'a'.the
gravitational force acting on a particle of mass m placed at the center is​

Answer 1

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