Question

An uniform lamina in the shape of a right angled triangle is shown in the figure. Find the coordinates of $\text{COM}$ of the lamina. Assume the origin to be at the intersection of x and y axes.

• A. $(\frac{a}{3},\frac{b}{3})$
• B. $(\frac{2a}{3},\frac{2b}{3})$
• C. $(\frac{2a}{3},\frac{b}{3})$
• D. $(\frac{a}{3},\frac{2b}{3})$

Answer 1

The correct option is C $(\frac{2a}{3},\frac{b}{3})$

For uniform triangular shaped lamina, its $\text{COM}$ lies at centroid ($\text{c}$) of triangle, which is at a distance of $\frac{h}{3}$ measured from the base.
where $h=$ height of triangle


From the figure shown above, the coordinates of $\text{COM}$ of lamina from the origin at $\text{O}$ is:
$x_{\text{CM}}=a-\frac{a}{3}=\frac{2a}{3}$
$y_{\text{CM}}=\frac{b}{3}$
Thus, coordinates of $\text{COM}$ are $(\frac{2a}{3},\frac{b}{3})$