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?
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.)
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?