The variation of density of a cylindrical thick and long rod is $\rho = \rho_0 \frac{x^2}{L^2}$. The position of its centre of mass from the $x = 0$ end is:

On what does the position of the center of mass of a rigid body depend?

The centre of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $d$ is:

Two particles of masses $200 \ g$ and $500 \ g$ are moving with velocities $10 \ \hat{i} \ m/s$ and $3 \ \hat{i} + 5 \ \hat{j} \ m/s$ respectively. The velocity of the center of mass of the system is:

The position of the centre of mass of a uniform semi-circular wire of radius $R$ placed in the $x-y$ plane with its centre at the origin and the line joining its ends as the $x$-axis is given by $\left(0, \frac{x R}{\pi}\right)$.
Then,the value of $|x|$ is ...... .

Three point masses $m_1 = 1.6 \, kg$,$m_2 = 2.0 \, kg$,and $m_3 = 2.4 \, kg$ are placed at the corners of a thin massless rectangular sheet $(1.2 \, m \times 1.0 \, m)$ as shown. The center of mass will be located at the point ........... $m$.