$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strike the rod with a velocity $v_0$ at point $C$ a distance $x$ from the centre $O$. The particle comes to rest after collision. The value of $x$, so that point $A$ of the rod remains stationary just after collision, is :

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

Particles of masses $m, 2m, 3m, ...... nm$ $grams$ are placed on the same line at distances $l, 2l, 3l,...., nl\, cm$ from a fixed point. The distance of the centre of mass of the particles from the fixed point (in centimetres) is

Two disc one of density $7.2\, g/cm^3$ and the other of density $8.9\, g/cm^3$ are of same mass and thickness. Their moments of inertia are in the ratio

Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat i\,\, + \,\,2\hat j\,\, + \,\,\hat k$ and  $-\,3\hat i\,\, - \,\,2\hat j\,\, + \,\,\hat k$, respectively. The centre of mass of this system has a position vector

In a rectangle $ABCD (BC = 2AB)$, the moment of inertia along which axis will be minimum ?