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Q.

A circular disc of diameter d and a square plate of side d are placed as shown in fig. The centre of mass of this combination from centre of disc is (both the object are having same mass per unit area)

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a

$\frac{4 d}{4 + π}$

b

$\frac{2 d + 3 π}{4 + π}$

c

$\frac{4 d}{3 + π}$

d

$\frac{3 d + 7 π}{4 + π}$

answer is A.

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Detailed Solution

For circular disc $m_{1} = k (π \frac{d^{2}}{4}); x_{1} = 0$

For plate, $m_{2} = d^{2}; x_{2} = d$

$X_{CM} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$\Rightarrow X_{cm} = \frac{4 d}{4 + π}$

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A circular disc of diameter d and a square plate of side d are placed as shown in fig. The centre of mass of this combination from centre of disc is (both the object are having same mass per unit area)