Q.
The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass $4kg$ . (The coordinates of the same are shown in the figure) are:
NTA AbhyasNTA Abhyas 2022
Solution:
$\left(\overset{ \rightarrow }{r}\right)_{c m}=\frac{2 \times \left(\frac{\hat{i}}{2} + \hat{j}\right) + 2 \times \left(\hat{i} + \frac{5 \hat{j}}{2}\right)}{4}$
$\overset{ \rightarrow }{r}_{c m}=\frac{3}{4}\hat{i}+\frac{7}{4}\hat{j}$
$\left(\overset{ \rightarrow }{r}\right)_{c m}=\frac{2 \times \left(\frac{\hat{i}}{2} + \hat{j}\right) + 2 \times \left(\hat{i} + \frac{5 \hat{j}}{2}\right)}{4}$
$\overset{ \rightarrow }{r}_{c m}=\frac{3}{4}\hat{i}+\frac{7}{4}\hat{j}$