
Please send your solution to
Ms. Valeria Pandelieva
641 Kirkwood Avenue
Ottawa, ON K1Z 5X5
It is very important that the front page contain your complete mailing address and your email address. The deadline for this set is December 21, 2002.
Notes: The sides of a rightangled triangle that are adjacent to the right angle are called legs. The centre of gravity or centroid of a collection of $n$ mass particles is the point where the cumulative mass can be regarded as concentrated so that the motion of this point, when exposed to outside forces such as gravity, is identical to that of the whole collection. To illustrate this point, imagine that the mass particles are connected to a point by rigid nonmaterial sticks (with mass 0) to form a structure. The point where the tip of a needle could be put so that this structure is in a state of balance is its centroid. In addition, there is an intuitive definition of a centroid of a lamina, and of a solid: The centroid of a lamina is the point, which would cause equilibrium (balance) when the tip of a needle is placed underneath to support it. Likewise, the centroid of a solid is the point, at which the solid ``balances'', i.e., it will not revolve if force is applied. The centroid, $G$ of a set of points is defined vectorially by