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

Three circular discs of same material and same thickness of radii $r, 2r$ and $3r$ are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is $2r$ and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is . . . . . . . (in $r$)

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

$A$ metre stick of mass $400 \ g$ is pivoted at one end and displaced through an angle $60^o$. The increase in its potential energy is ..... $J$.

Locate the centre of mass of the arrangement shown in the figure. The three rods are identical in mass and length.

If the linear density of a rod of length $3 \ m$ varies as $\lambda = 2 + x$,then the position of the centre of mass of the rod is: