Question

The sum of moments of all the particles in a system about the centre of mass is always

• A. maximum
• B. minimum
• C. infinite
• D. zero

Answer 1

The correct option is D zero

Using $\overrightarrow{r}=\frac{m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}+m_3\overrightarrow{r_3}}{M}$

Let origin be the centre of mass of the body which is represented by C. i.e $\overrightarrow{r}=0$

$⟹m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}+m_3\overrightarrow{r_3}=0$

Now net moment about C, $\overrightarrow{{\tau }_C}=m_{1}g\left(\overrightarrow{r_1}\right)+m_{2}g\left(\overrightarrow{r_2}\right)+m_{3}g\left(\overrightarrow{r_3}\right)$

$\overrightarrow{{\tau }_C}=g\left[m_1\right(\overrightarrow{r_1})+m_2(\overrightarrow{r_2})+m_3(\overrightarrow{r_3}\left)\right]=0$

Hence sum of moment of all the particles in the system about COM is always Zero.