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From a circular disc of radius R, anothe...

From a circular disc of radius `R`, another disc of diameter `R` is removed. Locate `c.m.` of the remaining portion.

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Here , from the larger disc, smaller disc is removed.
Larger disc : `m_(1) prop pi R^(2) rArr m_(1) = m , x_(1) = R`
`m_(2) prop pi(R //2)^(2) rArr m_(2) = (m)/(4) , x_(2) = (R )/(2)`
`c.m` of the remaining position
`x_(c.m.) = (m_(1) x_(1) - m_(2) x_(2))/(m_(1) -m_(2)) = (mR - (m)/(4) xx (R)/(2))/(m - (m)/(4) ) = ((7 mR)/(8))/(( 3m)/(4)) = (7 R)/(6)`
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Knowledge Check

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