a) Apply conservation of energy
Initial mechanical energy = final mechanical energy
Ui + Ki = Uf + Kf
-G*m^2/(4*R) + 0 = -G*m^2/(2*R) + 2*(1/2)*m*v^2
-G*m^2/(4*R) + G*m^2/(2*R) = m*v^2
G*m^2/(4*R) = m*v^2
G*m/(4*R) = v^2
v = sqrt(G*m/(4*R))
b) acceleration of each object, a = F/m
= G*m^2/(4*R)^2/m
= G*m/(16*R^2)
let t it the time taken.
use, s = u*t + (1/2)*a*t^2
2*R = 0 + (1/2)*(G*m/(16*R^2))t^2
t^2 = 64*R^3/(G*m)
t = 8*sqrt(R^3/(G*m))
c) t = 8*sqrt(0.1^3/(6.67*10^-11*7))
= 1.17*10^4 s
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