Q170 / 180 · COMEDK 2025 (10 May Shift 3) · Physics
Select the correct statement from the following: The position of the centre of mass of a system:
- ADoes not depend on the shape and size of the system
- BDepend on the choice of coordinates
- Correct answerCDepends on the distribution of its mass.
- DRemains the same in any translatory motion
Solution
The position of the centre of mass of a system of particles is defined by the vector $\vec{R}_{cm} = \dfrac{\sum m_i \vec{r}_i}{\sum m_i}$.
This definition shows that the location of the centre of mass is determined by the individual masses $m_i$ and their respective position vectors $\vec{r}_i$ relative to the chosen origin.
Since the position vectors $\vec{r}_i$ depend on the distribution of mass within the system, the centre of mass is fundamentally a property of the mass distribution of the body or system.
While the numerical coordinates of the centre of mass change if the origin of the coordinate system is shifted, the physical location of the centre of mass relative to the body itself is fixed by the mass distribution, making the statement regarding mass distribution the most fundamental physical description.
Answer: Depends on the distribution of its mass.
This definition shows that the location of the centre of mass is determined by the individual masses $m_i$ and their respective position vectors $\vec{r}_i$ relative to the chosen origin.
Since the position vectors $\vec{r}_i$ depend on the distribution of mass within the system, the centre of mass is fundamentally a property of the mass distribution of the body or system.
While the numerical coordinates of the centre of mass change if the origin of the coordinate system is shifted, the physical location of the centre of mass relative to the body itself is fixed by the mass distribution, making the statement regarding mass distribution the most fundamental physical description.
Answer: Depends on the distribution of its mass.
Hence, the correct answer is option: 'C'.