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Find the centre of mass of a unifrom (a)...

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))`

Text Solution

Verified by Experts

The correct Answer is:
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`
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