“Integration is zero for a point of homogeneous body' which is that point ? 

Obtain Newton's second law for system of particle and write it. 

How can general body be obtained ?

There is a rod of lenght $l$, mass $m$ lying on a fixed horizontal smooth table. A cord is led through a pulley, and its horizontal part is attached to one end of the rod, while its vertical part is attached to a block of mass $m_1$.  Assume pulley and the cord is ideal. The maximum possible acceleration of the rod's centre of mass $C$ (for all possible values of masses $m$ and $m_1$) at the moment of releasing the block $m_1$ is $\frac{g}{n}$.  Find the value of $n$

A solid sphere rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of sphere, then passes through over a solid cylinder and then is connected to block of mass $M$ as  shown in figure. If the system is released from rest then the speed acquired by block after it has fallen through distance $h$ is

What is rotational motion and  axis ?