Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d$,by what distance should the second particle be moved so as to keep the center of mass at the same position?

The distance of the centre of mass of a solid uniform cone from its vertex is $z_0$. If the radius of its base is $R$ and its height is $h$,then $z_0$ is equal to:

Three circular discs of same material and same thickness of radii $r, 2r$ and $3r$ are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is $2r$ and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is . . . . . . . (in $r$)

The linear mass density $(\lambda)$ of a rod of length $L$ kept along the $x$-axis varies as $\lambda = \alpha + \beta x$,where $\alpha$ and $\beta$ are positive constants. The centre of mass of the rod is at ..........

The distance between the two atoms in an $HCl$ molecule is approximately $1.27 \mathring{A}$ $(1 \mathring{A} = 10^{-10} \text{ m})$. The chlorine atom is $35.5$ times heavier than the hydrogen atom. The position of the center of mass from the hydrogen atom is approximately ..... $\mathring{A}$.

In the case of a system of two particles of different masses,the centre of mass lies