$A$ sphere of mass $m$ slides down a smooth inclined plane from a point $B$ at a height of $h$ starting from rest. The magnitude of the change in momentum of the particle between position $A$ (at the bottom of the incline) and $C$ (on the horizontal surface) is (assuming the angle of inclination of the plane is $\theta$ with respect to the horizontal):

$A$ body of mass $2 \, \text{kg}$ moving with a speed of $4 \, \text{m/s}$ makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two-body centre of mass is $\frac{x}{10} \, \text{m/s}$. Then the value of $x$ is ..... .

Assertion $(A)$: When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.
Reason $(R)$: Energy can change from one form to another but the total energy is always conserved.
Which of the following is true?

$A$ bullet of mass $10 \ g$ pierces through a plate $A$ of mass $500 \ g$ and then gets embedded into a second plate $B$ of mass $1.49 \ kg$ as shown in the figure. Initially,the two plates $A$ and $B$ are at rest and move with the same velocity after the collision. The percentage loss in the initial kinetic energy of the bullet when it is between the plates $A$ and $B$ is . . . . . . (Neglect any loss of material of the plates during the collision).

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the ball starts moving up the inclined face of the wedge and rises to a height $h$. Suppose the particle,when it reaches the horizontal surface again,has a velocity $v_1$ with respect to the ground,and the wedge has a velocity $v_2$. Choose the correct statement$(s)$.

$A$ 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 ..... .