In the figure shown, find the out centre of mass of a system of a uniform circular plate of radius 3R from O in which a hole of radius R is cut whose centre is at 2R distance from the centre of large circular plate

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$\frac{R}{4}$

none of these

$\frac{R}{5}$

$\frac{R}{2}$

answer is C.

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Detailed Solution

$\begin{array}{l} x_{C M} = \frac{A_{1} x_{1} - A_{2} x_{2}}{A_{1} - A_{2}} \\ = \frac{π (3 R)^{2} (0) - (π R^{2}) (2 R)}{π (3 R)^{2} - π R^{2}} = - \frac{R}{4} \end{array}$

$∴ Distance of centre of mass from origin = \frac{R}{4}$

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