Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices  $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of  mass of the particles are

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$, the speed of centre of mass of the system is

Three particles each of mass $m$ are placed at the corners of equilateral triangle of side $l$ 

Which of the following is lare correct?

A wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road, a small jump of mud separates from the wheel at its highest point $B$ and drops at point $C$ on the road. The distance $AC$ will be

Two uniform thin identical rods $AB$ and $CD$ each of mass $M$ and length $L$ are joined so as to form a cross as shown. The moment of inertia of the cross about a bisector line $EF$ is (Line $EF$ is perpendicular to $ABCD$ plane)

If a solid sphere is rolling, the ratio of its rotational energy to the total kinetic energy is given by