A semicircular portion of radius 'r' | vedclass

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Question

$A_{1}=2 r 	imes r=2 r^{2}$

$A_{2}=\frac{\pi r^{2}}{2}$

$\mathrm{x}_{1}=\frac{\mathrm{r}}{2} \quad \mathrm{x}_{2}=\frac{4 \mathrm{r}}{3 \pi}$

Vedclass · Accepted Answer

$\frac{{2r}}{3{(4 - \pi )}}$

Vedclass · Answer

$A_{1}=2 r 	imes r=2 r^{2}$

$A_{2}=\frac{\pi r^{2}}{2}$

$\mathrm{x}_{1}=\frac{\mathrm{r}}{2} \quad \mathrm{x}_{2}=\frac{4 \mathrm{r}}{3 \pi}$

$\mathrm{x}_{\mathrm{cm}}=\frac{2 \mathrm{r}^{2} 	imes \frac{\mathrm{r}}{2}-\frac{\pi \mathrm{r}^{2}}{2} 	imes \frac{4 \mathrm{r}}{3 \pi}}{2 \mathrm{r}^{2}-\frac{\pi \mathrm{r}^{2}}{2}}$

$=\frac{r\left[1-\frac{2}{3}ight]}{\left[\frac{4-\pi}{2}ight]}=\frac{2 r}{3[4-\pi]}$

A semicircular portion of radius $'r'$ is cut from a uniform rectangualr plate as shown in figure. The distance of centre of mass $'C'$ of remaining plate, from point $'O'$ is

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