When does a body (system) have different centre of gravity and centre of mass ? 

Three masses are placed on the $x-$axis $: 300\, g$ at origin, $500 \,g$ at $x = 40\, cm$ and $400\, g$ at $x = 70\, cm.$ The distance of the centre of mass from the origin is ....... $cm$

From a circular disc of radius $R$ a triangular portion is cut (see fig.). The distance of  $COM$ of the remaining disc from centre of disc $O$ is:-

A circular hole of radius $\left(\frac{ a }{2}\right)$ is cut out of a circular disc of radius $'a'$ as shown in figure. The centroid of the remaining circular portion with respect to point $'O'$ will be :

Four particles $A, B, C$ and $D$ with masses $m_A=m, m_B=2m, m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

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 is moved, so as to keep the centre of mass at the same position?