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A disc of radius R is placed on a square...

A disc of radius R is placed on a square plate of edge 4R made up of the same sheet with their planes parallel such that any two adjacent sides ofsquare touch the disc. Find the distance of the centre of mass of the system from the centre of square plate?

Text Solution

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Let us consider that `sigma` = mass / area of the sheet
Mass of disc `= m_(1) = pi R^(2) sigma` & mass of square plate `= 16 R^(2)sigma`
By geometry OP. = OP = R
`C_(1)C_(2)=2sqrt(2)R-sqrt(2)R=sqrt(2)R`
`therefore X_(cm)=(sqrt(2)Rxx pi R^(2)sigma + 0 xx 16 R^(2)sigma)/((16+pi)R^(2)sigma)=(sqrt(2)pi R)/(16+pi)` along
`C_(1)C_(2)` from `C_(1)`
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