BOOK 01- MATHEMATICAL PROBLEMS. 



6 being the angle between their directions. Prove that the 

 moment of the principal couple is 



cPQ sin 6 



1229. If a system of forces be reduced to two, one of which 

 F acts along a fixed straight line j then will 



1 cos c sin 

 F = ~1T' """' 



6 being the angle which the given straight line makes with the 

 central axis, c the shortest distance between them, ^ the result- 

 ant force, and G the principal couple. 



1230. If a system of forces be reduced to two at right angles 

 to each other, the shortest distance between their lines of action 



26r 



cannot be less than . 

 K 



1231. If a system of forces be reduced to two P, Q, and the 

 shortest distances of their lines of action from the central axis be 

 x, y respectively ; then will 



1232. Two forces act along the straight lines 



o: = a, 2/ = tana; x = a, y = 

 prove that their central axis lies on the surface 



the coordinates being rectangular. 



1233. Two forces given in magnitude act along two given 

 non-intersecting straight lines, a third force given in magnitude 

 acts through a given point, and the three have a single resultant; 

 prove that the line of action of the third force must lie on a 

 certain cone of revolution. 



