Mention the position of centre of mass of ring, disc and spheres. 

Two particle of masses $1\,kg$ and $3\,kg$ have position vector $2\hat i + 3\hat j + 4\hat k$ and $ - 2\hat i + 3\hat j - 4\hat k$ respectively. The centre of mass has a position vector

Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is :

A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ much below the centre of mass of the cabin. A close observation of the motion of $A$ and $B$ will reveal that

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

A circular hole of radius $\left(\frac{ a }{2}\right)$ is cut out of a circular disc of radius $'a'$ as shown in figure. The centroid of the remaining circular portion with respect to point $'O'$ will be :