Answer
The kinetic energy of each body is $~~\frac{Gm^2}{2R_i}$
Work Step by Step
We can use conservation of energy to find the total kinetic energy:
$K_f+U_f = K_i+U_i$
$K_f = 0+U_i - U_f$
$K_f = U_i - U_f$
$K_f = (-\frac{Gm^2}{R_i}) - (-\frac{Gm^2}{0.5~R_i})$
$K_f = \frac{Gm^2}{R_i}$
The total kinetic energy is $~~\frac{Gm^2}{R_i}$
By symmetry, the kinetic energy of each body will be half of the total kinetic energy.
We can find the kinetic energy of each body:
$K = \frac{Gm^2}{2R_i}$
The kinetic energy of each body is $~~\frac{Gm^2}{2R_i}$
