Two particles $P$ and $Q$ have mass $4.0 \mathrm{kg}$ and $1 \mathrm{kg}$ respectively. They are projected along a vertical line with velocity $u_P=$ $20 \mathrm{m} {\mathrm{s}}^{-1}$ and $u_Q=5 \mathrm{m} {\mathrm{s}}^{-1}$ when separation between them was $60 \mathrm{m}. P$ was projected vertically up while $Q$ was projected vertically down. Calculate the maximum height attained (in $\mathrm{m}$ ) by the centre of mass of the system of two particles, measured from the initial position of $P.$ Assume that the particles do not collide and that the ground is far below their point of projection $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right].$

Two blocks of masses $\mathrm{m}=2 \mathrm{kg}$ and $M=8 \mathrm{kg}$ are connected to a spring of force constant $k=1\mathrm{kN}/\mathrm{m}.$ The spring is compressed by $20 \mathrm{cm}$ and the two blocks are held in this position by a string. The system is placed on a horizontal smooth surface and given a velocity $u=3 \mathrm{m}/\mathrm{s}$ perpendicular to the spring. The string snaps while moving. The speed (in $\mathrm{m}/\mathrm{s}$ ) of the block of mass $\mathrm{m}$ when the spring regains its natural length is

Three identical particles are placed on a horizontal smooth table, connected with strings as shown. The particle $B$ is imparted a velocity $v_0=9 \mathrm{m}/\mathrm{s}$ in horizontal direction perpendicular to the line $ABC.$ The speed (in $\mathrm{m}/\mathrm{s}$ ) of particle $A$ when it is about to collide with $C.$