Answer:
a = 3.21 10⁻⁸ m / s²
, The correct answer is E
Explanation:
For this exercise we will use Newton's second law, where the force is the gravitational attraction force, the attached diagram shows the forces and their components in a horizontal and vertical coordinate system, due to the symmetry of the equilateral triangle the horizontal components be annulled and the two vertical components add up; let's write Newton's education for the vertical axis (Y)
2
= m a
Let's use trigonometry to find the components
sin 60 =
/ F
= F sin60
2 F sin60 = m a
The gravitational force equation is
F = G m M / r
The mass of the entire sphere is equal to m = M and the distance between the spheres is the side of the equilateral triangle
F = G m² / L²
We replace
2 (G m² / L²) sin60 = m a
a = 2 G m / L² sin 60
Let's calculate
a = 6.67 10⁻¹¹ 50 / 0.30² sin 60
a = 3.21 10⁻⁸ m / s²
The correct answer is E