A Triangular Plate

Q. 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.

1. $(\frac{a}{3},\frac{2b}{3})$
2. $(\frac{a}{3},\frac{b}{3})$
3. $(\frac{2a}{3},\frac{2b}{3})$
4. $(\frac{2a}{3},\frac{b}{3})$

Q. Find the height of the center of mass of the equilateral triangular lamina from the side $\text{AB}$ as shown in figure. Given, side of the triangular lamina is $3\text{m}$.

1. $\frac{3}{\sqrt{2}}\text{m}$
2. $\frac{\sqrt{3}}{2}\text{m}$
3. $\frac{\sqrt{2}}{3}\text{m}$
4. $\sqrt{3}\text{m}$

Q. Find the height of the center of mass of the equilateral triangular lamina from the side $\text{AB}$ as shown in figure. Given, side of the triangular lamina is $3\text{m}$.

1. $\sqrt{3}\text{m}$
2. $\frac{3}{\sqrt{2}}\text{m}$
3. $\frac{\sqrt{3}}{2}\text{m}$
4. $\frac{\sqrt{2}}{3}\text{m}$

Q. In the adjoining fig. along which axis the M.I. of the triangular lamina will be maximum- (given that $AB<BC<AC)$

1. AB
2. BC
3. CA
4. For all axis

Q. The center of mass of a triangle with a uniform mass density coincides with

1. Circumcenter
2. Centroid
3. Incenter
4. Othrocenter

Q. 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.

1. $(\frac{a}{3},\frac{b}{3})$
2. $(\frac{2a}{3},\frac{2b}{3})$
3. $(\frac{2a}{3},\frac{b}{3})$
4. $(\frac{a}{3},\frac{2b}{3})$

Q. Find the height of the center of mass of the equilateral triangular lamina from the side $\text{AB}$ as shown in figure. Given, side of the triangular lamina is $3\text{m}$.

1. $\sqrt{3}\text{m}$
2. $\frac{3}{\sqrt{2}}\text{m}$
3. $\frac{\sqrt{3}}{2}\text{m}$
4. $\frac{\sqrt{2}}{3}\text{m}$