BUMFUH. 



A solid is formed by the revehtfai of the i 

 vo y^.ooj** round tne axis of x; shew ih* 

 tance of the centre of gravity of an/ sqgmtt 



a. The segment U supposed cut off by a 



cular to the 



48. Find the centre of gravity of the wr^m of the solid 

 f + y-Sax, cut off bj the pUne x-a 



,.<-,- 



49. Applv Gnldinna't theorem to find the rolim* of the 

 fnutnm of a right COM in term* of it, h;mde and U* radii 



50. Find the tnrfrce and the Tolumc of the aolid 

 bj the revolution of a cycloid round it* 



51. A segment of a 



subtends an angle of 90* at the centre; find tne 

 volume of the solid generated. 



-. 



v v* 



51 An ellipse whose eccentricity U ^ revolves aboot 



any tangent line. Prove that the volaae generaiail by OM 

 portioninto which the ellips. u minor 



varies in vcwcly as the volume generated by the 



58. A plane area moves in snch a manner as to be always 

 normal to the curve along which its centre of gravity moms; 

 prove that the volume generated it mil to the me* area 

 length of the path of the esAtre of gravity. 



Hence find the volume of a cycloidal tibe whose 

 section is of constant area. 



