(2) \(a_0=\frac{\sqrt{3}GM}{4d^2};v=\sqrt{\frac{2GM}{d}}\)
f = gravitational force on mass m; at a due to O1 or O2
F = net gravitational force on mass m at a = 2f cosθ = 2 (Gmm/4d2) x √3/2
\(=\frac{\sqrt{3}GMm}{4d^2}\)
a0 = initial acceleration of mass m at A = F/m
\(=\frac{\sqrt{3}GM}{4d^2}\)
Ee = initial total energy of mass m at A
= \(-2[\frac{GMm}{2d}]\)
Ef = Total final energy of mass m at O
\(=\frac{1}{2}mv^2+(-\frac{2GMm}{d})\)
From law of conservation of energy, Ee = Ef