

m. 



(2) The density of a r v.-uit > a. the ?i th 



the distance from the axis; find the centre of gravity of the 

 cone. 



Let OAB be the right-angled triangle which liy r 

 9 



round Ox generates the cone. Let PS and QR lie drawn 

 parallel to the axis of x at distances y and y + Ay r. 

 lively. Let 



OA = h, angle BOA = a. 



Then 



OM= y cot a, PS=h-y cot a. 



The volume of the cylindrical shell generated }>y the revolu- 

 tion of PQR8 round Ox is ultimately 



2-Try Ay (A y cot a). 



Its density is /iy", where /x is constant; therefore, its mass is 

 27r/iy' l+i Ay (7* y cot a). 



The distance of its centre of gravity from is ultimately (see 

 135, Ex. 1) 



i (OH + OA), that is J (7* + y cot a) ; 



therefore x 



/ 

 _ J o 



h Una 



(h - y cot a) i (A + y cot a) <fy 



/. tan a 



y cot a) Jy 



A Una 



h tan o 



and the integrations can be easily performed. 



