120 CENTER OF GRAVITY 



of the points D and C, these being weighted in the ratio w : W. 

 Denoting this center of gravity by G, we have, from the formula 



on treating the line ADCB as the axis of x and taking A as origin, 



_ W-AC + w-AD 



W + w 

 _W(l-a) + \ wl 



W+w 



EXAMPLES 



1. Weights of 3 pounds are placed at each of three corners of a square, and 

 a weight of 5 pounds at the fourth corner. Find their center of gravity. 



2. From one corner of a cardboard square of edge 6 inches, a square of edge 

 3 inches is cut. Find the center of gravity of the remainder. 



3. A thin rod of weight 6 ounces and length 6 inches is nailed on to a circle 

 of cardboard of weight 6 ounces and radius 6 inches so that its two ends are on 

 the circumference of the circle. Find the center of gravity of the whole. 



4. A bicycle wheel of diameter 26 inches weighs 3 pounds. Each spoke is of 

 length 11 inches, and starts from the hub at a distance of i inch from the cen- 

 tral axis of the wheel. If one spoke is taken out, find the center of gravity of 

 the wheel. 



5. A hammer has for handle a wooden cylinder, length 8 inches, radius 

 | inch, weight 8 ounces, and for head an iron cylinder, from which a hollow is 

 cut into which the handle exactly fits, the handle coming through so as to be 

 exactly flush with the iron. The head is of length 3 inches, radius 1| inch, and 

 weight 3 pounds. Find the approximate position of the center of gravity. 



6. A box, without lid, is made of 1-inch wood so as to have internal dimen- 

 sions 12 x 12 x 12 inches. Find the position of its center of gravity. 



7. A uniform thin rod 28 inches in length is bent so that the two parts, of 

 lengths 12 and 16 inches, are at right angles to one another. Find the center of 

 gravity. 



8. A uniform wire is bent into the form of a triangle. Show that the center 

 of gravity of the wire coincides with the center of the circle inscribed in the 

 triangle formed by joining the middle points of the sides. 



9. A T-square is made of cedar of uniform density, the crosspiece being of 

 dimensions 6 x 2 x \ inches, and the arm being of dimensions 8 x 1| x } inches. 

 The crosspiece is cut away so that the under surface of the instrument is 

 plane. Find the position of the center of gravity of the whole. 



