Two bodies $A$ and $B$ have masses $M$ and $m$ respectively,where $M > m$,and they are at a distance $d$ apart. Equal forces are applied to each of them so that they approach each other. The position where they hit each other 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

Four particles of masses $m, 2m, 3m, 4m$ are placed at the corners of a square of side $a$ as shown in the figure. Find the coordinates of the center of mass.

The 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:

The centre of mass of a homogeneous semi-circular plate of radius $r$ is located at $A$ as shown in the figure. The distance $OA$ is

Three particles of masses $20 \, g$,$30 \, g$,and $50 \, g$ have velocities $10 \, \hat{i}$,$10 \, \hat{j}$,and $10 \, \hat{k}$ respectively. The velocity of the center of mass of these three particles is: