A)
B)
C)
D)
Correct Answer: D
Solution :
 |
| By symmetry, \[{{x}_{CM}}=0\] |
| \[dm=\frac{m}{\pi }d\theta \] |
| \[{{y}_{CM}}=\frac{\int{ydm}}{\int{dm}}=\int_{0}^{\pi }{\frac{\left( r\sin \theta \right)\left( \frac{m}{\pi }d\theta \right)}{\int_{0}^{\pi }{dm}}}\] |
| \[=\frac{\frac{rm}{\pi }.\int_{0}^{\pi }{\sin \theta }d\theta }{m}=\frac{2r}{\pi }\] |
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