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A system of particles are located on the x-axis with masses, in kilograms, 7, 12, 2, 10, and 3 whose coordinates are −4, 2, 5, -2, and 3. Find the center of mass of the system. The length of a rod is 4 meters and the linear density is (x+2) kg/m from any point x from one end. Find the center of mass of the rod. The total mass of a rod 2 meters long is 18 kg. If the linear density varies directly as the cube of the distance of the point from one end, find the linear density at the midpoint of the rod. 3 A rod is L meters long and the center of mass of the rod is at the point L meters from the left end. If the measure of the linear density at a point is proportional to a power of the measure of the distance of the point from the left end and the linear density at the right end is 20 kg/m, find the linear density at a point x meters from the left end. (Leithold, 1996)