Murthy 



and 



z = z - [x* cos0 + (z' + h ) sin0]0 + [x' sin0 - (z 1 + h ) cos B ~\$' 

 Also, since 



r 1 = (x' cos 8+ y 1 sin0) 1 + y 1 j + (z* cos0 - x" sin0) & 

 we derive after substitution and carrying out the vector product 

 + z - [x 1 cos + (z 1 + h ) sin0] 



+ [x 1 sin0 - (z' + h ) cos ] \i 



+ ^(z' cos 6 - x 1 sin0)[x + |(z' + h ) cos - x' sin0)} 



vflr 



** 



\(z' cos 6 - x 1 sin0)[x + |(z' + h ) cos - x' sin0)> 



( 1-2 



- <x' cos + (z' + h ) sin0 > ] 



- (x 1 cos0+ z' ein0) [- g + z - <x' cos0 + (z 1 + h ) sin0S0 



+ jx 1 sin0 - (z 1 + h ) cos0] ]Jj 



]>j 



y' 1 x + [(z' + h ) cos - x' sin0] 



+ [x' cos0 - (z' + h ) sin0] 0* 

 G 



Now, we have the following results : 



W 



dm 



z' dm = m z' 



- /// 



f 

 "I 



/jfjf x' y' dm = 0,/// y' z' 



(ii) 

 (iii) 



(iv) 



(z 1 + h_) dm = 

 G 



x' dm = m x' = 



y' dm = m y',,, = 



since the z'-axis passes 

 through the C. G. 



dm = due to the lateral sym- 

 metry 



208 



