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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 are object are having same mass per unit area)

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a

$\frac{4 d}{4 + π}$

b

$\frac{4 d}{3 + π}$

c

$\frac{2 d + 3 π}{4 + π}$

d

$\frac{3 d + 7 π}{4 + π}$

answer is A.

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Detailed Solution

Question Image

From the figure

$x_{com} = \frac{(σ \times π \frac{d^{2}}{4}) (0) + d^{2} \times d}{σ \times π \frac{d^{2}}{4} + {σd}^{2}}$

$x_{com} = \frac{{σd}^{3}}{σ (\frac{π + 4}{4}) d^{2}}$

$x_{com} = \frac{4 d}{π + 4}$

Hence the correct answer is $\frac{4 d}{π + 4} .$

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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 are object are having same mass per unit area)