Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$ . If the radius of its base is $R$ and its height is $h$ then $z_0$ is equal to

A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by

Weights of $1\,g,2\,g.....,100\,g$ are suspended from the $1 \,cm, 2 \,cm, ...... 100\, cm, \,marks$ respectively of a light metre scale. Where should it be supported for the system to be in equilibrium ...... $cm$ mark.

Define centre of mass. 

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

The position vector of three particles of masses $1\, kg, 2\, kg$ and $3\, kg$ are $\overrightarrow {{r_1}}  = (\widehat i + 4\widehat j + \widehat k)\,m,\overrightarrow {{r_2}}  = (\widehat i + \widehat j + \widehat k)\,m$ and $\overrightarrow {{r_3}}  = (2\widehat i - \widehat j - 2\widehat k)\,m$  respectively. The position  vector of their centre of mass is