The centre of mass of a body

Three identical spheres each of diameter $2\sqrt{3} \text{ m}$ are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the spheres is removed,then the shift in the position of the centre of mass of the system is

$A$ rod of length $3\, m$ has a mass per unit length directly proportional to the distance $x$ from one of its ends. The center of gravity of the rod from that end will be at ........ $m$.

Mention the centre of mass of three particles which are not in line but have equal masses.

What do you mean by mass element $dm$?

Find the centre of mass of a uniform $L$-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is $3 \; kg$.