The centre of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $d$ is:

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

The figure below shows a shampoo bottle in a perfect cylindrical shape. In a simple experiment,the stability of the bottle filled with different amounts of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle $\theta$ depict the critical angular displacement resulting in the bottle losing its stability and tipping over. Choose the graph that correctly depicts the fraction $f$ of shampoo filled ($f=1$ corresponds to completely filled) versus the tipping angle $\theta$.

Consider a system of two particles of masses $m_1$ and $m_2$. If mass $m_1$ is pushed towards the center of mass of the system by a distance $d$,by what distance should the mass $m_2$ be displaced so that the center of mass of the system remains unchanged?

Three identical spheres,each of mass $1 \ kg$,are kept as shown in the figure,touching each other,with their centres on a straight line. If their centres are marked $P, Q, R$ respectively,the distance of the centre of mass of the system from $P$ is

$A$ ladder is leaning against a smooth wall and is free to slide on a frictionless floor. Which of the following diagrams correctly represents the path of the center of mass of the ladder?