A ball $P$ of mass 0.5 kg moving with a velocity of $10 \mathrm{~ms}^{-1}$ collides with another ball $Q$ of mass 1 kg at rest. If the coefficient of restitution is 0.4 , the ratio of the velocities of the balls $P$ and $Q$ after the collision is

A circular plate of radius $r$ is removed from a uniform circular plate $P$ of radius $4 r$ to form a hole. If the distance between the centre of the hole formed and the centre of the plate $P$ is $2 r$, then the distance of mass of the remaining portion from the centre of the plate $P$ is

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