Question

The coordinates of centre of mass of the following quarter circular arc is –

• A. $\left( \frac{r}{2},\frac{r}{2} \right)$
• B. $\left( \frac{2r}{3},\frac{2r}{3} \right)$
• C. $\left( \frac{2r}{\pi},\frac{2r}{\pi} \right)$
• D. $\left( \frac{4r}{\pi},\frac{4r}{\pi} \right)$

Answer 1

Answer: (C)

$\left( \frac{2r}{\pi},\frac{2r}{\pi} \right)$

Answer 2

dm = lRdq = $\frac{2m}{\pi}$dq

\ x_cm = $\frac { 1 } { \mathrm {~m} }$ $\int_{}^{}{xdm}$= $\frac{1}{m}\int_{0}^{\pi/2}{R\cos\theta\frac{2m}{\pi}d\theta}$

Similarly y_cm = $\frac{1}{m}\int_{0}^{\pi/2}{R{sin.}\theta\frac{2m}{\pi}d\theta}$