$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x$ such that $\frac{\mu mg}{K} < x < \frac{2\mu mg}{K}$,and then released. Which of the following laws/principles of physics can be applied to the spring-block system?

$A$ block of mass $\sqrt{2} \, kg$ is released from the top of an inclined smooth surface as shown in the figure. If the spring constant of the spring is $100 \, N/m$ and the block comes to rest after compressing the spring by $1 \, m$,then the total distance travelled by the block along the incline before it comes to rest is ......... $m$.

$A$ particle which is experiencing a force,given by $\vec F = 3\hat i - 12\hat j$,undergoes a displacement of $\vec d = 4\hat i$. If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement,what is its kinetic energy (in $J$) at the end of the displacement?

Two monkeys with the same mass stand on a branch at height $h$ above the horizontal jungle floor. Monkey $A$ steps off the branch holding the end of an inextensible rope of length $L$ whose other end is tied to another branch at height $H$,lets go at the bottom of the swing,and falls freely to the floor,as shown below. Monkey $B$ steps off and falls straight downward. Then,neglecting air resistance but not the tension in the rope,the total work $W$ done on each monkey and the speed $v$ with which each hits the floor are as follows:

$A$ body of mass $0.5\; kg$ travels in a straight line with velocity $v=a x^{3/2}$ where $a=5\; m^{-1/2} s^{-1}$. What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m$?

$A$ ball at rest is dropped from a height of $12 \,m$. It loses $25 \%$ of its kinetic energy on striking the ground and bounces back to a height '$h$'. Then the value of '$h$' is (in $\,m$)