Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be ............. $Joule$.

$A$ bullet of mass $0.012\;kg$ and horizontal speed $70\;m\;s^{-1}$ strikes a block of wood of mass $0.4\;kg$ and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also,estimate the amount of heat produced in the block.

$A$ particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory,it makes a completely inelastic collision with another identical particle,which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is :

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially,$S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision,$S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision:

Match the items in Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Work done is zero	$(a)$ By gravitational force (when body moves down)
$(2)$ Work done is positive	$(b)$ Against gravitational force (when body moves up)
$(3)$ Work done is negative	$(c)$ By centripetal force

In the diagram shown,there is no friction at any contact surface. Initially,the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.