A ball of mass 1.2 kg moving with a velocity of $12 \mathrm{~ms}^{-1}$ makes one-dimensional collision with anothe stationary ball of mass 1.2 kg . If the coefficient of restitution is $\frac{1}{\sqrt{2}}$, then the ratio of the total kinetic energy of the balls after collision and the initial kinetic energy is

An alphabet $T$ made of two similar thin uniform metal plates of each length $L$ and width $a$ is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its centre of mass from the horizontal surface is

Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \mathrm{~ms}^{-1}$. $12 \mathrm{~ms}^{-1}$ and $8 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of particles is

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2 m$ at rest. If the coefficient of restitution is 0.4 the ratio of the velocities of the spheres $A$ and $B$ after collision is