If a long spring is stretched by $0.02\, m$, its potential energy is $U$. If the spring is stretched by $0.1\, m$ then its potential energy will be

$A$ 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 work done by spring force is 

A block of mass $m$ is pushed against a spring whose spring constant is $k$ fixed at one end with a wall. The block can slide on a frictionless table as shown in figure. If the natural length of spring is $L_0$ and it is compressed to half its length when the block is released, find the velocity of the block, when the spring has natural length

Initially spring is in natural length and both blocks are in rest condition. Then determine Maximum extension is spring. $k=20 N / M$

A ball of mass $m_1$ falls from height $h_1$ from rest to strike a spring of force constant $K$, which forces another ball of mass $m_2$ to jump on a horizontal floor at a height $h_2$ below from it. Find the horizontal distance at which ball of mass $m_2$ strikes from the position of start :- [Spring does not move]

Pulley and spring are massless and the friction is absent everwhere. $5\, kg$ block is  released from rest. The speed of $5\, kg$ block when $2\, kg$ block leaves the contact  with ground is (take force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2)$