A square plate of edge 'a' and a circular disc of the same diameter are placed touching each other at the midpoint of an edge of the plate as shown in the figure. If mass per unit area for the two plates are same then find the distance of the center of mass of the system from the center of the disc.

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Solution

mass of m1 $m_{1} = d^{2} m$
mass of m2 $m_{2} = π d^{2} \frac{m}{4}$
$[(d ² m d + π (d ² / 4) m x 0) / (d ² m + π (d ² / 4) m), (0 + 0) / (M ₁ + M ₂)]$
$[d ³ m / d ² m (1 + π / 4), 0]$
$[4 d / (π + 4), 0]$

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mass of m1 m1=d2mmass of m2 m2=πd2m4[(d²md+π(d²/4)mx0)/(d²m+π(d²/4)m),(0+0)/(M₁+M₂)][d³m/d²m(1+π/4),0][4d/(π+4),0]

mass of m1 $m_{1} = d^{2} m$
mass of m2 $m_{2} = π d^{2} \frac{m}{4}$
$[(d ² m d + π (d ² / 4) m x 0) / (d ² m + π (d ² / 4) m), (0 + 0) / (M ₁ + M ₂)]$
$[d ³ m / d ² m (1 + π / 4), 0]$
$[4 d / (π + 4), 0]$