Figure shows a disc of radius R = 20 cm with a portion of it removed symmetrically. The removed part is a disc of radius R/2. The removed part is now placed in contact with the larger disc. Centres of all the three discs lie on x-axis. Disc has uniform mass distribution. With respect to origin at centre of larger disc find x-coordinate of system (in cm).

Engineering

Physics

Center of Mass

Question

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M = mass of complete disc = πR²σ ; σ-mass per unit area.
m = mass of removed part = $\frac{{πR}^{2}}{4} σ$

$x_{cm} = \frac{M \times 0 + (- m) (\frac{R}{2}) + (m) \frac{3 R}{2}}{M + (- m) + m} = \frac{mR}{M} = 5 cm$

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