Mention the position of centre of mass of particles of equal mass. 

If the linear density of a rod of length $3m$ varies as $\lambda = 2 + x$, then the position of centre of gravity of the rod is :

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\frac{\alpha}{R}$ form the centre of the bigger disc. The value of a is $\alpha $ 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?

Two point masses $m$ and $M$ are separated by a distance $L$. The distance of the centre of mass of the system from m is

A man inside a freely falling box throws a heavy ball towards a side wall. The ball keeps on bouncing between the opposite walls of the box. We neglect air resistance and friction. Which of the following figures depicts the motion of the centre of mass of the entire system (man, the ball and the box)?