A hole is drilled through the center of Earth and elevator car is installed inside?

Question

The car departs from the surface (1km above sea level), and after quick initial acceleration continues to move towards the center of the earth at constant velocity 100 m/s.

Few seconds into constant velocity phase of the trip, when elevator just crosses sea level, a passneger drops elactic ball on the floor, which continues to bounce elastically from the floor with initial period 1s.

As the car approaches the center of the earth, period of bouncing gradually increases.

What is the period of bouncing half-way towards the center of earth?

Answer 1

Yowch!!
That's a good one. Calculate the amount of mass 'above' the plane cutting through a sphere, then calculate the gravitational acceleration of the mass 'below' minus the mass 'above' and use that for the net acceleration on the ball.

You is gonna be doing a couple of integrals on that one.

Have fun ☺

Doug

Answer 2

Grav. accel a is proportional to radius (ref.).
Period t is proportional to sqrt(1/a).
So halfway down t = sqrt(2) s.