The co-ordinates of the centre of mass of a uniform $L$ shaped plate of mass 3 kg shown in the figure is

Three blocks $A, B$ and $C$ are arranged as shown in the figure such that the distance between two successive blocks is 10 m . Block $A$ is displaced towards block $B$ by 2 m and block $C$ is displaced towards block $B$ by 3 m . The distance through which the block $B$ should be moved, so that the centre of mass of the system does not change is

Two balls each of mass 250 g moving in opposite directions each with a speed $16 \mathrm{~ms}^{-1}$ collide and rebound with the same speeds. The impulse imparted to one ball due to the other is

A block of mass 10 kg moving with a speed of $5 \hat{\mathrm{i}} \mathrm{ms}^{-1}$ on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass 4 kg moves with a speed of $10 \hat{\mathbf{i}} \mathrm{~ms}^{-1}$, then the velocity of the second piece is