Question

A scalene triangular lamina of uniform mass density and negligible thickness has one of its vertices at the origin. The position vectors of its other two vertices are $\overrightarrow{a}$ and $\overrightarrow{b}$ . The location of its centre of mass will be

• A. $\frac{\overrightarrow{a}+\overrightarrow{b}}{2}$
• B. $\frac{\overrightarrow{a}+\overrightarrow{b}}{3}$
• C. $\frac{2(\overrightarrow{a}+\overrightarrow{b})}{3}$
• D. $\frac{3(\overrightarrow{a}+\overrightarrow{b})}{4}$

Answer 1

The correct option is B $\frac{\overrightarrow{a}+\overrightarrow{b}}{3}$

Since, centre of mass of triangle is basically centroid of triangle.
The centroid of the triangle having vertices $\overrightarrow{0},$$\overrightarrow{a}$ and $\overrightarrow{b}$ is given by $\frac{\overrightarrow{0}+\overrightarrow{a}+\overrightarrow{b}}{3}=\frac{\overrightarrow{a}+\overrightarrow{b}}{3}$