STATICS. 



The length of each rod being a, and the pegs at equal dist- 

 ances b; prove that there will be three positions of equilibrium if 



1246. A rectangular board is supported with its plane verti- 

 cal by two smooth pegs, and rests with one diagonal parallel to 

 the line joining the pegs ; prove that the other diagonal will be 

 vertical. 



1-17. A rectangular board whose sides are a, b, is supported 

 with its plane vertical on two smooth pegs in the same horizontal 

 line at a distance c; prove that the angle made by the side a 

 with the vertical when in equilibrium is given by the equation 



2c cos 20 = b cos - a sin 0. 



1248. A portion of a parabola, cut off by a focal chord in- 

 clined at an angle a to the axis, rests with its chord horizontal on 

 two smooth pegs in the same horizontal line at a distance c ; prove 

 that the hitus rectum of the parabola is c>J5 sin* a. 



1219. A uniform rod AS of length 2a is freely moveable 

 about A ; a smooth ring of weight P slides on the rod and hits 

 attached to it a fine string, which, passing over a pulley at a 

 i b vertically above A, supports a weight Q hanging freely: 

 iiml tin- jH.siti ..n <>f equilibrium of the system; and prove that, if 

 in this position the rod and string be equally inclined t 

 \rrtic;il, 



1250. A uniform rod, of length c, rests with one end on a 

 smooth elliptic arc, whoso major axis is horizontal, and with thu 

 other on a smooth vertical plane at a h from the c> 



of the ellip.se; prove that, if $ be the angle made by the rod 



with thu horizon, 



tan = -r tan <, where a cos < + h = c cos 0. 

 Explain the result Vhen a = 26 = c, A = 0. 



17-2 



