Three masses, $m, 2m,$ and $3m$ are located at coordinates $(a,0), (4a,0),$ and $(-a,0)$, respectively. What are the coordinates of the center of mass of the system?

A system of three identical particles of mass $1 \ kg$ each are moving, as shown in the diagram below.

What is the net momentum of the system of these three particles?

A sphere of mass $2 \ kg$ is dropped from a height of $2 \ m$. On collision with the floor, the sphere rebounds with a speed of $3 \ m/s$. The magnitude of change in the momentum of the sphere is,

Two particles of masses $1.5 \ kg$ and $1.25 \ kg$ are moving along different directions, as shown below.

After the collision, they combine and move with velocity $\overrightarrow{V}$. Find the magnitude of $\overrightarrow{V}$.

The net force acting on a system of interacting particles is $0 \ N$. Which of the below statements is TRUE regarding the system?

An object moves due to force $f(t)$ acting on it. Calculate the impulse on the object from time $t=0 \ s$ to $t=2 \ s$ if $f(t)=2e^{-t}$.

A projectile of mass $4 \ kg$ falling vertically down explodes in mid-air. The projectile breaks into three parts, as shown below.

How far from the original line of motion does the $0.6 \ kg$ part fall?

Which force-time graph shows the largest momentum change?

A non-uniform rod of linear density $ρ(x) = Ax^2$ (where $A$ is a positive constant) extends from $x=0$ to $x=L$. Find the center of mass of the rod.

Two balls of mass $m$ and $2m$, moving towards each other, suffer a head-on elastic collision. The velocities of the two balls before the collision are $-u$ and $3u$, respectively. What is the velocity of ball of mass $m$ after the collision if $2m$ continues to move in the same direction as before?

A radioactive particle disintegrates into two smaller particles, as shown in the diagram below.

If the original particle was moving to the right with a speed of $v_1$, then what should be the size of angle $y$?

An isolated system of four identical interacting particles is moving steadily along the $+x$ direction. The velocity of the center of mass of the system is equal to $1 \ m/s$. If the velocity of three particles is $(2\skew{2.5}\hat{i} +2\skew{4}\hat{j} \ ) \ m/s, (\skew{2.5}\hat{i} + 2\skew{4}\hat{j} \ ) \ m/s,$ and $(-3\skew{2.5}\hat{i} – 5\skew{4}\hat{j} \ ) \ m/s$, then what is the velocity of the fourth particle?

Questions 13, 14, and 15 are based on the below information:

A ball of mass $0.2 \ kg$ is moving towards a wall with a speed of $6.5 \ m/s$. It undergoes a partial inelastic collision and bounces back with a smaller velocity, as shown below.

What is the value of $u$ if the ball loses 24% of its energy due to the collision?

A ball of mass $0.2 \ kg$ is moving towards a wall with a speed of $6.5 \ m/s$. It undergoes a partial inelastic collision and bounces back with a smaller velocity, as shown below.

Calculate the average force $f_{avg}$ acting on the ball during the collision with the wall if the time of contact is $0.25 \ s$.

A ball of mass $0.2 \ kg$ is moving towards a wall with a speed of $6.5 \ m/s$. It undergoes a partial inelastic collision and bounces back with a smaller velocity, as shown below.

If the actual variation in force is given in the graph below, then what is the value of $f_{max}$?