Write the meaning of homogeneous bodies.

Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat{i}+2\hat{j}+\hat{k}$ and $-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The magnitude of the position vector of the centre of mass of this system will be equal to the magnitude of which of the following vectors?

The centre of mass of two particles lies:

Three identical spheres,each of mass $2 M$,are placed at the corners of a right-angled triangle with mutually perpendicular sides equal to $4 \ m$ each. Taking the point of intersection of these two sides as the origin,the magnitude of the position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$,where the value of $x$ is . . . . . .

Two identical uniform rectangular blocks (with longest side $L$) and a solid sphere of radius $R$ are to be balanced at the edge of a heavy table such that the centre of the sphere remains at the maximum possible horizontal distance from the vertical edge of the table without toppling as indicated in the figure. If the mass of each block is $M$ and of the sphere is $M/2$,then the maximum distance $x$ that can be achieved is

The position of the centre of mass of a cube of uniform density will be at