An elevator shaft is drilled directly through the Earth along its diameter, running from near Buenos Aires to near Shang

[answerhappygod]

An elevator shaft is drilled directly through the Earth along
its diameter, running from near Buenos Aires to near
Shanghai. An elevator car with a physicist inside is dropped
through the shaft. Show that the motion of the elevator car
is simple harmonic motion and find an expression for the time
period of the motion in terms of ρ (the density of Earth)
and G. From the time period, calculate the shortest time
for the physicist to reach the Shanghai end if dropped in the
Buenos Aires end at t=0.
For this problem assume that the radius of the Earth
is RE=6.37×106 m, that the mass of the Earth
is ME=5.972×1024 kg, that the density of the Earth is
uniform, and that the Earth is a perfect sphere. (Hint: you
will need to have an expression for how g depends on
radius r inside the Earth.)
Give your answer to exactly 3 significant figures, in
minutes.
G=6.67×10−11 N m2/kg2.