$A$ small ball $B$ of mass $m$ is suspended with light inelastic string of length $L$ from $a$ block $A$ of same mass $m$ which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle $\theta$ from equilibrium position & then released. The displacement of centre of mass of $A+ B$ system till the string becomes vertical is

The centre of mass of a non uniform rod of length $L$ whose mass per unit length $\lambda $ varies as $\lambda \ =\ \frac{{k\,.\,{x^3}}}{L}$ where $k$ is a constant & $x$ is the distance of any point on rod from its one end, is at distance (from the same end)

The coordinates of the positions of particles of mass $7,\,4{\rm{  and 10}}\,gm$ are ${\rm{(1,}}\,{\rm{5,}}\, - {\rm{3),}}\,\,{\rm{(2,}}\,5,7{\rm{) }}$ and ${\rm{(3, 3, }} - {\rm{1)}}\,cm$ respectively. The position of the centre of mass of the system would be

The position vector of the centre of mass $\vec r\, cm$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

The centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not. What is the qualitative meaning of small and extended in this regard ? For which of the following two coincides ? A building, a pond, a lake, a mountain ? 

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 :