Estimate the mass of the gravitational field of the Earth. What would the size of a cube of water with the same mass?

Use the following info (the real info is complex, but the following is close enough):

Relative density of inner core = 13, radius = 400 km

Relative density of outer core = 11, radius = [...]

A ball is dropped from a height of 1 m on to a hard surface. Each time it bounces, the ball loses half of it’s energy. How long does the ball bounce for? Is there a paradox?

A cyclist cycled a mile in 4 minutes against the wind. He returned in 3 minutes. How long would it have taken if there had been no wind?

Assume that rolling resistance is independent of speed and that the wind force is proportional to e^v² where v is the cyclist’s air-speed.

Make reasonable assumptions.

A smooth sphere of radius r is glued to a table top. A small mass is resting at the exact top dead centre. It is given a very small disturbance and starts to slide over the surface of the sphere. How far below the top of the sphere does the object get before separating from the sphere?

Ignore the [...]

Two boys walking in the woods decided to take a shortcut through a railroad tunnel. when they had walked two-third of the way through the tunnel, their worst fears were realized. A train was coming from the opposite direction, nearing the tunnel entrance. The boys panicked and each ran for a different end of the [...]

A wire is tied to a normal bicycle pedal that is stationary at the bottom of its arc. If someone pulls this wire backwards (while another person lightly holds the seat to keep the bike balanced), will the cycle move forward, backward or not at all? Assume that the wheels don’t slip and that the bicycle [...]

What is the probability that, in any breath that you take, that at least one molecule of it was exhaled by Archimedes in his last dying breath?

Assume that a breath contains 10^22 molecules and that the atmosphere contains 10^44 molecules.

Using a standard pack of 52 playing cards, pile them up to make the top card hang out above the bottom card. What is the furthest overhang distance that can be achieved? Would you do better on the Moon?

No glue or other such ideas. Just stack the cards up.

Take oil and water in a beaker. The oil floats in a separate layer above the water. In which direction should one accelerate the beaker to mix the oil and water? (An emulsion can be taken to mean a mixture for our purposes here.) And hey, we need heavy funda to go with your response.