EXAMI'I 



t from nn rjiiilal'-r:il trianirl 



of the. square coinciding with a side of tin- trianirlr; iY.un 

 jiiilateral triangle which remains another squaiv [fl rut, 

 i. ad \nfinihtm: lind t: <f irravity >f thr sum 



of tin 1 squares. 



J7. Kind the centre of crravitv of the aiva rnntaim-d lie- 

 tin- curves if ax and y*=2axx\ which is above 



thr axis of x. r> 7. 1. ",7744 - a 



Results. * = a._- 4o ; J. ( 



28. Find the centre of gravity of the area encl < 1 by 

 the curve r = a (1 + cos 0). /.'> *ult. x 



20. Find the centre of gravity of the area included by a 



loop of the curve r = a cos 20. 7 _ P28a\/2 



Jiesuit. x- 



..<>. Find the centre of gravity of the area included 1-y a 

 loop of the curve r = a cos 30. , _ 81 j3a 



. -:- 



31. The locus of the centre of gravity of all equal seg- 

 :s cut off from a parabola is an equal parabola. 



32. Find the centre of gravity of a segment of a circle. 



Find the centre of gravity of the area included by 

 the curves if^ax and x 2 = by. 



Result, x = 3 n ga*^f y 



84 Find the centre of gravity of a portion of an equi- 

 lateral hyperbola bounded by the curve, the transverse axis, 

 and a radius vector drawn from the centre. 



Results, g 





, 

 9 3 log (#' + #') -3 log a' 



where x, ;/' arc the co-ordinates of thr point of intersection of 

 the ( I the bounding radius vctor. 



