SYSTEM OF MASSES 119 



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87. It is clear that if we suspend a rigid body or system of 

 bodies by a string, the center of gravity must be vertically below 

 the string. For all the forces acting on the system reduce to two, 

 the tension of the string and the weight acting at the center 

 of gravity, and in equilibrium these two must act along the 

 same line. 



In the same way it will be seen that if a body is placed on a 

 point in such a way as to balance in equilibrium on this point, 

 then the center of gravity must be vertically above the point. 



88. A few simple instances of the position of the center of 

 gravity have been mentioned in 77. These were as follows : 



(a) the center of gravity of a uniform rod is at its middle point ; 



(b) the center of gravity of a uniform circular disk, circular 

 ring, or sphere is at the center; 



(c) the center of gravity of a cube or parallelepiped is at the 

 center (i.e. the intersection of the diagonals). 



89. It is easy to find the center of gravity of a system of bodies 

 when the center of gravity of each of the component parts is known. 

 For, regarding the weight of each of the bodies as a single force 

 acting through its center of gravity, we have a number of parallel 

 forces in action, and on compounding these according to the rules 

 already explained, the line of action of the resultant determines 

 the line along which the total weight will act. Thus the center 

 of gravity of the whole system of bodies will be the centroid of 

 the centers of gravity of the separate bodies, weighted 

 according to the masses of these bodies. 



90. For instance, let us suppose we require to find the 

 center of gravity of a pendulum which consists of a wire, 

 of length / and weight w, to which is affixed a circular bob 

 of weight W, the center of the circle being at a distance a 

 from the end of the wire. Let AB be the wire, C the center 

 of the bob, and D the middle point of the wire. The center 

 of gravity of the wire will be at D and that of the bob at C, ] 



so that the center of gravity of the whole will be at the centroid 



