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Q.

A geometry consists of a square and a disc as shown in figure. It is made up of an iron sheet of uniform density. The y-coordinate of centre of mass of the geometry with respect to point O is

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a

$\frac{4 a + 3 π a}{4 + 3 π}$

b

$\frac{4 a + 3 π a}{4 + π}$

c

$(4 + 3 π) a$

d

$3 a$

answer is A.

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Detailed Solution

For two dimensional bodies, $y_{c m} = \frac{A_{1} y_{1} + A_{2} y_{2}}{A_{1} + A_{2}} = \frac{(4 a^{2}) (a) + π a^{2} (3 a)}{4 a^{2} + π a^{2}}$

$y_{c m} = \frac{4 a + 3 π a}{4 + π}$

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