Question

If the origin of co-ordinate system lies at the centre of mass, the sum of the moments of the masses of the system about the centre of mass

• A. may be greater than zero
• B. may be less than zero
• C. may be equal to zero
• D. is always zero

Answer 1

The correct option is D is always zero

If the origin of the coordinate system is at the centre of the mass then ${\overrightarrow{R}}_{CM}=0$, which in turn implies that ${\sum }_i{m}_i\overrightarrow{r_i}=0\text{as}{\overrightarrow{R}}_{CM}=\frac{{\sum }_i{m}_i\overrightarrow{r_i}}{{\sum }_i{m}_i}$
$(m_i\overrightarrow{r_i}$ represents the moment of a mass about the origin or the centre of mass).
Hence, the correct answer is option (d).