The centre of mass of a system of particles does not depend on

$A$ uniform rod of mass $400 \ g$ and length $1 \ m$ is pivoted at one end. It is displaced by an angle of $60^o$. The increase in its potential energy is ....... $J$.

Infinite numbers of blocks are placed on a table edge as shown in the diagram. What is the minimum value of $L$ so that the blocks are just going to topple over the table?

$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

Three masses are placed on the $x-$axis: $300 \, g$ at the origin,$500 \, g$ at $x = 40 \, cm$ and $400 \, g$ at $x = 70 \, cm$. The distance of the centre of mass from the origin is ....... $cm$.

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