A) \[\frac{4a+3\pi a}{4+\pi }\]
B) \[\frac{4a+3\pi a}{4+3\pi }\]
C) \[(4+3\pi )a\]
D) \[3a\]
Correct Answer: A
Solution :
For two dimensional bodies \[{{X}_{cm}}=\frac{{{A}_{1}}{{Y}_{1}}+{{A}_{2}}{{Y}_{2}}}{{{A}_{1}}+{{A}_{2}}}=\frac{(4{{a}^{2}})(a)+\pi {{a}^{2}}(3a)}{4{{a}^{2}}+\pi {{a}^{2}}}\] \[\Rightarrow \]\[{{X}_{cm}}=\frac{4a+3\pi a}{4+\pi }\] (The X - coordinate of the centre of mass is always zero for this shape).
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