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ques 1, 5 and 9

Asked by rbhatt16 14th October 2017, 8:54 PM
Answered by Expert
Answer:
Question No.1
 
begin mathsize 12px style M o m e n t space o f space I n e r t i a space space I space equals space integral subscript 0 superscript L d m cross times r squared space
S i n c e space d e n s i t y space i s space n o t space u n i f o r m comma space d m space equals space rho left parenthesis r right parenthesis space d r space left parenthesis d e n s i t y space i s space f u n c t i o n space o f space d i s tan c e space f r o m space h i n g e space p o i n t right parenthesis

w h e r e space rho left parenthesis r right parenthesis space equals space rho subscript 0 space open parentheses 1 plus r over L close parentheses

h e n c e space I space equals space integral subscript 0 superscript L rho subscript 0 space open parentheses 1 plus r over L close parentheses cross times r squared space d r
end style
begin mathsize 12px style I space equals space rho subscript 0 space integral subscript 0 superscript L r squared d r space plus space space rho subscript 0 over L space integral subscript 0 superscript L r cubed d r space equals space rho subscript 0 space L cubed over 3 plus space rho subscript 0 L cubed over 4 space equals space rho subscript 0 space 7 over 12 L cubed end style 
begin mathsize 12px style M a s s space o f space t h e space r o d space space M space equals space integral subscript 0 superscript L d m space equals space space integral subscript 0 superscript L rho left parenthesis r right parenthesis d r space equals space space integral subscript 0 superscript L rho subscript 0 left parenthesis 1 plus r over L right parenthesis d r space equals space rho subscript 0 left parenthesis L space plus space L over 2 right parenthesis space equals space 3 over 2 rho subscript 0 L end style
 
begin mathsize 12px style S o space M o m e n t space o f space I n e r t i a space I space equals space 3 over 2 L rho subscript 0 space 7 over 18 L squared space space equals space 7 over 18 M L squared end style 
 
 
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Answered by Expert 16th October 2017, 4:38 PM
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