Question

The centre of mass of triangle shown in figure has coordinates:

• A. $x = \frac{h}{2},y = \frac{b}{2}$
• B. $x = \frac{b}{2},y = \frac{b}{2}$
• C. $x = \frac{b}{3},y = \frac{h}{3}$
• D. $x = \frac{h}{3},y = \frac{b}{3}$

Answer 1

Answer: (C)

$x = \frac{b}{3},y = \frac{h}{3}$

Answer 2

We can assume that three particles of equal mass m are placed at the corners of triangle

$\overset{\rightarrow}{r_{1}} = 0\widehat{i} + 0\widehat{j},\mspace{6mu}\overset{\rightarrow}{r_{2}} = b\widehat{i} + 0\widehat{j}$ and $\overset{\rightarrow}{r_{3}} = 0\widehat{i} + h\widehat{j}$

$\therefore$ $\overset{\rightarrow}{r_{cm}} = \frac{m_{1}\overset{\rightarrow}{r_{1}} + m_{2}\overset{\rightarrow}{r_{2}} + m_{3}\overset{\rightarrow}{r_{3}}}{m_{1} + m_{2} + m_{3}} = \frac{b}{3}\widehat{i} + \frac{h}{3}\widehat{j}$

i.e. coordinates of centre of mass is $\left( \frac{b}{3},\frac{h}{3} \right)$