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Find the centre of mass of a uniform pla...

Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii `R_1 and R_2`.

Text Solution

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The correct Answer is:
A, B, C, D
`y_(CM)=(A_1y_1-A_2y_2)/(A_1-A_2)`
`=((pib^2//2)(4b//3pi)-(pia^2//2)(4a//3pi))/((pib^2//2)-(pia^2//2))`
`=(4)/(3pi)[(b^3-a^3)/(b^2-a^2)]`
`=(4)/(3pi){(a^2+ab+b^2)/(a+b)}`
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