A $4 \mathrm{~kg}$ mass is suspended as shown in figure. All pulleys are frictionless and spring constant $k$ is $8 \times 10^3 \mathrm{Nm}^{-1}$. The extension in spring is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A 3 kg block is connected as shown in the figure. Spring constants of two springs $k_1$ and $k_2$ are $50 \mathrm{Nm}^{-1}$ and $150 \mathrm{Nm}^{-1}$ respectively. The block is released from rest with the springs unstretched. The acceleration of the block in its lowest position is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Two bodies $A$ and $B$ of masses $2 m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2 u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at height equal to half of the maximum height reached by body $A$ is

A body of mass 2 kg collides head on with another body of mass 4 kg . If the relative velocities of the bodies before and after collision are $10 \mathrm{~ms}^{-1}$ and $4 \mathrm{~ms}^{-1}$ respectively. The loss of kinetic energy of the system due to the collision is