Four masses $1 \ kg, 1 \ kg, 2 \ kg$ and $2 \ kg$ are placed at the four corners $P, Q, R$ and $S$ of a square of side $a$ respectively. The center of mass of the system will be farthest from which of the following?

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

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.

In an $HCl$ molecule,the distance between the nuclei of the two atoms is $1.27 \ \mathring A$. The $Cl$ atom is approximately $35.5$ times heavier than the $H$ atom. The center of mass of this molecule will be at a distance of approximately ....... $\mathring A$ from the center of the $H$ atom.

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles,and each of the two line segments is $m$. The mass of the ink used to draw the outer circle is $6m$. The coordinates of the centres of the different parts are: outer circle $(0,0)$,left inner circle $(-a, a)$,right inner circle $(a, a)$,vertical line $(0,0)$ and horizontal line $(0,-a)$. The $y$-coordinate of the centre of mass of the ink in this drawing is

An isolated particle of mass $m$ is moving in a horizontal plane $(x-y)$ along the $x$-axis,at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. An instant later,the smaller fragment is at $y = +15 \ cm$. The larger fragment at this instant is at