Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is:

$A$ truck pulls a mass of $1200 \ kg$ at a constant speed of $10 \ m/s$ on a level road. The tension in the coupling is $1000 \ N$. The power used on the mass will be ..... . When the truck moves on an incline of $1 \ m$ rise in $6 \ m$ length,the tension will be ..... .

$A$ box of mass $1 \ kg$ is placed on a horizontal surface of length $1 \ m$. $A$ force of $8 \ N$ is applied to move it horizontally by $1 \ m$,while simultaneously,its vertical height is increased by $2 \ m$. What is the total work done in Joules? (Take $g = 10 \ m/s^2$)

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

$A$ 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 :

The diagram shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R \text{ & } S)$ is minimum at $t = 2 \text{ ms}$.
$(III)$ The mass of $R$ was greater than the mass of $S$.