The Eiffel tower in Paris has including the tv antenna an height of 321 meter. It is made out of 7 million kg steel. Somebody would like to build a scale model of this tower with a weight of 1 kg. How tall will this scale model be?

At the same time a block of iron and an equally heavy iron sphere are released from the top of a slope. Assume that the friction between the slope has a negligible effect on the velocity of the block and the sphere. Which of the two will be down first?

According to homeopaths the effect of a homeopathic medicin is indicated by a dilution factor. Their theory is that if a substance is diluted more, the effect of it will increase. The dilution factor of a homeopathic medicin consists of a number and a character. An X or D indicates that the substance is diluted a number times 10. A C stands for a factor 100. As an example, 6 X indicates that the substance is diluted 10^6 = 1,000,000 times. Typical dilution factors of homeopathic medicins lie between 6 X and 30 X. Suppose you bought a litre of homepathic medicin with a dilution factor of 30 X. Assume that water was used for the dilution proces, and that the molecules of the substance are about as big as the water molecules (smaller is almost impossible, since water is one of the smallest molecules). How many molecules of the substance can you find in your bottle. And how many litres would you need to buy to be sure that you will have at least one molecule of the substance?