Respuesta :
Answer:
F = 0 N
Explanation:
For this exercise the force is gravitational that is given by
F = G m₁ m₂ / r₁₂²
We use Newton's second law to find the total force
F = F₁ₐ + f₂ₐ + F₃ₐ + F₄ₐ
Where
F₁ₐ is the force between sphere 1 or the central sphere, the distance is
r₁ₐ = √ (L /)²+ (L / 2)² = L / 2 √ 2
This distance is the same for all spheres, because the spheres are in the corner of a cube,
Let's explicitly write the force
F₁ₐ = G m₁ mₐ / L √2 / 2
[We can see that the modulus of each force is the same because the masses have the same value and with or the line of action is in the diagonals of the cube the force is annulled two by two
F₁ₐ = F₃ₐ
F₂ₐ = F₄ₐ
Therefore the total force on the central sphere is zero
F = 0 N
