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Question #1

Hole through the Earth

Suppose you could drill a hole through the center of the Earth. If you drop a ball, how long does it take to pop up at the other end?

Question #2

Resistor Cube

Twelve identical 330 Ω resistors are soldered together to form a cube. What resistance would an ohmmeter measure if the leads are placed at A and D? (Hint: Use symmetry to split the currents up at junction points.)

Question #3:

Snowboarder on Ice

Starting from rest at the top, a snowboarder slides down a hemispherical mound of ice of radius R. Assuming the ice is frictionless, at what angle Θ from the vertical will the snowboarder lose contact with the ice?