$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

To an observer $A,$ the net work done on the block is

Two masses $m_1 = 2\,kg$ and $m_2 = 5\,kg$ are moving on a frictionless surface with velocities $10\,m/s$ and $3\,m/s$ respectively. An ideal spring is attached on the back of $m_2$ . The maximum compression of the spring will be ............... $\mathrm{m}$

A spring of spring constant $ 5 \times 10^3$ $ N/m$  is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\,cm$ is .............. $\mathrm{N-m}$

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

According to observer $B$, the potential energy of the spring increases

As shown in figure there is a spring block system. Block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0\,cm$ . The spring constant is $500\,N/m$ . When released, calculate the distance where it will hit the ground $4\,m$ below the spring ? $(g = 10\,m/s^2)$

Two identical blocks $A$ and $B$ each of mass $m$ resting on the smooth horizontal floor are connected by a light spring of natural length $L$ and spring constant $K$. A third block $C$ of mass $m$ moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$.The maximum compression in the spring is