## tisdag 6 april 2010

### Claude Allegre and Gravity

The claim by Claude Allegre that a light tennis ball and a heavy petanque (boule ball) will reach the ground at the same time if dropped from the top of the tower of Pisa, has caused some discussion and questioning. Can it be true? Yes, it can if the balls are scaled so that the quantity of radius times density, is the same for the two balls.  This is under the assumption the air drag scales like density times radius squared, while mass scales like the third power of the radius.

This means that the heavy ball must have both a smaller radius, and smaller mass than the tennis balls (and not as would seem more natural that the radius or mass are equal). The quotient of the radii thus should be equal to the inverse of the quotient of densities, while if instead the mass is kept the same, the quotient of the radii would be equal to the third root of the inverse density quotient. A tennis ball and a small petanque could thus fall equally fast. If the density of the petanque is 10 times that of the tennis ball, then the petanque radius would be 10 times smaller, and its mass 100 times smaller: A small petanque.