In general form what are the coordinates of centre of mass of a rigid body.

Write the difference between centre of gravity and centre of mass of a body?

A projectile of mass $3\,m$ explodes at highest point of its path. It breaks into three equal parts. One part retraces its path, the second one comes to rest. The distance of the third part from the point of projection when it finally lands on the ground is ........$m.$ (The range of the projectile was $100\,\,m$  if no explosion would have taken place)

Two semicircular rings of linear mass densities $\lambda $ and $3\lambda $ and of radius $R$ each are joining to form a complete ring. The distance of the centre of the mass of complete ring from its geometrical centre is

Infinite rods of uniform mass density and length $L, L/2, L/4....$ are placed one upon another upto infinite as shown in figure. Find the $x-$ coordinate of centre of mass

A rigid body can be hinged about any point on the $x$ -axis. When it is hinged such that the hinge is at $x$, the moment of inertia is given by $I = 2x^2 - 12x + 27$ The $x$ -coordinate of centre of mass is