G2 EXAMPLES 



B top of _ r s vertically, sii] 



a ' lieam will iv~t in all pi.siti.ni.s if 



n /', IT, and a. 



If a weight be suspended IV ;tn mity of i 



moveable about the other extremity J. whieh reman, 

 and a string of given length be attached to any {mint // in 

 the rod, and also to a fixed point C above A, and in t 

 ;ual line with it, then the tension of the B\ 

 sely as the distance A //. 



26. One end of a uniform beam is placed on the gr 

 against a fixed obstacle, and to the other end is attached a 

 string which runs in a horizontal direction to a fixed point in 

 the same vertical line as the obstacle, and passing I'm 



il kept in tension by a weight IF suspended at its extremity, 

 heam being thus held at rest at an inclination of 45 to 

 the horizon. Shew that if the string were attached to the 

 centre instead of to the end of the beam, and passed over the 

 same fixed point, a weight = ^2\\' would keep t. in 



the same position. 



27. Two equal beams AB, A C connected by a hin^e at 

 A are placed in a vertical plane with their extremities H. 



>n a horizontal plane; they are kept from falling by 

 !ngs connecting B and C with the middle points of the, 

 opposite sides ; shew that the ratio of the tension of each 

 .-tring to the weight of each beam 



= JV(8cot f + cosec'0), 

 6 being the inclination of each beam to the horizon. 



28. One end of a string is attached to a beam at the point 

 B, and the other end is fastened to the highest point A of a 

 fixed sphere of radius r. If the points of contact <f the I., -am 

 and string trisect the quadrant AC, shew that the distance 

 between B and the centre of gravity of the beam must be 



J-V3). 



29. A heavy rod can turn freely about a fixed him:'' at 

 extremity, and it carries a heavy rin.u p which is attached 



to a fixed point in the same horizontal plane with tin; hinge 

 by means of a string of length equal to the distance between 

 the point and the hinge. Find the position in which the 

 rod will rest 



