Question 5: Centre of Mass and Rotational Motion

Question

Select the correct statement from the following: The position of the centre of mass of a system :

Accepted Answer

The correct choice is Option D.
Explanation:
By definition the centre of mass of a system of point masses $m_i$ at positions $\mathbf r_i$ is
$$\mathbf R_{\rm cm} \;=\;\frac{1}{M}\sum_i m_i\,\mathbf r_i\,,\quad M=\sum_i m_i.$$
This formula shows that $\mathbf R_{\rm cm}$ depends directly on how the mass is distributed (the values of each $m_i$ and their positions $\mathbf r_i$).
Shape and size only matter insofar as they affect that mass distribution.
Although the numerical coordinates of $\mathbf R_{\rm cm}$ change if you pick a different origin (Option B), the physical location of the centre of mass for a given distribution is determined solely by the masses and their arrangement.
Hence, Ã¢ÂÂDepends on the distribution of its massÃ¢ÂÂ is the fundamental property.

Answer

Remains the same in any translatory motion

Answer

Depend on the choice of coordinates

Answer

Does not depend on the shape and size of the system

Answer

Depends on the distribution of its mass.

Centre of Mass and Rotational Motion

Select the correct statement from the following: The position of the centre of mass of a system :

Choose the correct answer: