i n space t h e space a b o v e space s o l t i o n comma space t o space f i n d space t h e space c e n t r e space o f space m a s s space o f space u n i f o r m space s e m i minus c i r c u l a r space d i s c comma space h o w space t h e space y space c o o r d i n a t e space i s space t a k e n space a s space left parenthesis 2 r divided by straight pi right parenthesis ? ? ?
 

Asked by commonuc | 9th Dec, 2015, 08:41: PM

Expert Answer:

From the figure,
begin mathsize 12px style straight y space equals space integral subscript 0 superscript straight pi 1 over straight m straight y space dm straight y space equals 1 over straight m space integral subscript 0 superscript straight pi space end superscript rsin space straight theta space straight m over straight pi space dθ space equals space fraction numerator 2 straight r over denominator straight pi end fraction end style
 
 
 
In case of disc, we consider ring element. Hence, half disc which is of width dy and radius y = r
Y coordinate of the disc can be treated as Y coordinate of it's centre of mass .

In the case of half disc centre of mass is located at the height, begin mathsize 12px style fraction numerator 2 straight y over denominator straight pi end fraction space equals space fraction numerator 2 straight r over denominator straight pi end fraction end style from the centre of ring.

Answered by Priyanka Kumbhar | 10th Dec, 2015, 03:26: PM