A body of mass 2 kg moving with a velocity of $(\hat{\mathrm{i}}+$ $2\hat{\mathrm{j}}-$ $3\hat{\mathrm{k}})$ ms${}^{-1}$ collides with another body of mass 3 kg moving with a velocity of $(2\hat{\mathrm{i}}+$ $\hat{\mathrm{j}}+$ $\hat{\mathrm{k}})$ ms${}^{-1}$ . If they stick together, the velocity in ms${}^{-1}$ of the composite body will be:

1. $\frac{1}{5}(8\hat{i}+$ $7\hat{j}-$ $3\hat{k})$

2. $\frac{1}{5}(-4\hat{i}+$ $\hat{j}-$ $3\hat{k})$

3. $\frac{1}{5}(8\hat{i}+\hspace{0.17em}\hat{\mathrm{j}}-$ $\hat{\mathrm{k}})$

4. $\frac{1}{5}(-4\hat{i}+$ $7\hat{j}-$ $3\hat{k})$

Two equal masses, \(m_1\) and \(m_2,\) moving in the same straight line at velocities +3 m/s and –5 m/s respectively, collide elastically. Their velocities after the collision will be:

1. +4 m/s for both

2. –3 m/s and +5 m/s

3. –4 m/s and +4 m/s

4. –5 m/s and +3 m/s

A smooth sphere of mass M, moving with velocity u, directly collides elastically with another sphere of mass m at rest. After the collision, their final velocities are V and v, respectively. The value of v is:

1. \(\frac{2 um}{m}\)

2. \(\frac{2 um}{M}\)

3. \(\frac{2 u}{1 + {m \over M}}\)

4. \(\frac{2 u}{1 + {M \over m}}\)

Which of the following remains unchanged (for the system) during an inelastic collision?

A car of mass 100 kg and traveling at 20 m/s collides with a truck weighing 1 tonne traveling at 9 km/h in the same direction. The car bounces back at a speed of 5 m/s. The speed of the truck after the impact will be:

1.  11.5 m/s

2.  5 m/s

3.  18 m/s

4.  12 m/s

A body of mass 2 kg moving with a velocity of 3 m/s collides with a body of mass of 1 kg moving with a velocity of 4 m/s in the opposite direction. If the collision is head-on and completely inelastic, then the wrong statement is:

1. Both bodies move together with a velocity (2/3) m/s.

2. The momentum of the system is 2 kg-m/s throughout.

3. The momentum of the system is 10 kg-m/s.

4. The loss of KE for the system is (49/3) J.

On a frictionless surface, a block of mass \(M\) moving at speed \(v\) collides elastically with another block of the same mass \(M\) which is initially at rest. After the collision, the first block moves at an angle \(\theta\) to its initial direction and has a speed \(\frac{v}{3}\). The second block’s speed after the collision will be:
1. \(\frac{2\sqrt{2}}{3}v\)
2. \(\frac{3}{4}v\)
3. \(\frac{3}{\sqrt{2}}v\)
4. \(\frac{\sqrt{3}}{2}v\)

A body of mass m moving at a certain speed suffers a perfectly inelastic collision with a body of mass M at rest. The ratio of the final kinetic energy of the system to the initial kinetic energy will be:

1. \(m \over {m + M}\)

2. \(M \over {m + M}\)

3. \({m + M} \over m\)

4. \({m + M} \over M\)

Five balls are placed one after another along a straight line as shown in the figure. Initially, all the balls are at rest. Then the second ball is projected with speed ${\mathrm{v}}_0$ towards the third ball. Mark the correct statement(s). (Assume all collisions to be head-on and elastic):
     

1. The total number of collisions in the process is 5.

2. The velocity of separation between the first and fifth ball after the last possible collision is ${\mathrm{v}}_{0.}$

3. Finally, three balls remain stationary.

4. All of the above are correct.

A stone is projected from a horizontal plane. It attains maximum height, 'H', and strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall where the ball will strike will be: