Find the centre of mass of a unifrom (a) half-disc,(b) quarter-disc.
A. `(R,R/pi)`
B. `0,0`
C. `(4R/pi,0)`
D. `(0,(4R)/(3pi))`
A. `(R,R/pi)`
B. `0,0`
C. `(4R/pi,0)`
D. `(0,(4R)/(3pi))`
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Correct Answer – D
The half disc can be supposed to be consisting of a large number of semicircular rings of mass `dm` and thickness `de` and radii ranging from
`r=0` to `r=R`
`x_(CM)=1/mint_(0)^(R)xdm=1/mint_(0)^(R)0 dm=0`
`y_(cm)=1/Mint_(0)^(R)ydm=1/Mint_(0)^(R)(2r)/mxx((2M)/(R^(2))rdr)=((4R)/(3pi))`
Surface area of ring `=pirdr`
`dm=(2M)/(R^(2))rdr`