Three interacting particles of masses \(1.0~\text{kg}\), \(2.0~\text{kg}\) and \(4.0~\text{kg}\) have each a velocity of \(1~\text{ms}^{-1}\)${\mathrm{}}^{}$ magnitude along the positive direction of \(x\), \(y\) and \(z\)-axis respectively. Due to forces of interaction third particle stops and the velocity of second particle becomes \(2\hat j+\hat k~\text{ms}^{-1}\), the velocity of the first particle is:
1. \(4\hat i+\hat j+\hat k\)
2. \(\hat i-2\hat j+2\hat k\)
3. \(2\hat i+3\hat j-\hat k\)
4. \(-\hat i+3\hat j+\hat k\)

Two bodies having masses $m_1$ and $m_2$ and velocities $u_1$ and $u_2$ collide form a composite system. If $m_1$$u_1$ + $m_2$$u_2$ = 0 ($m_1$ $\ne$$m_2$), the velocity of composite system will be

1.  $u_1$ - $u_2$

2.  $u_1$ + $u_2$

3.  $\frac{u_1 + u_2}{2}$

4.  Zero

Two identical balls marked \(2\) and \(3\) in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked \(1\) moving initially with a speed \(v\) as shown in the figure. Assume the collision is elastic, then mark out the correct statement.

A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of 3 kg mass is 16 m/s. The velocity of 6 kg mass is

1. 4 m/s

2. 8 m/s

3. 16 m/s

4. 32 m/s

Two perfectly elastic particles A and B of equal mass traveling along the line joining them with velocities 15 m/s and 10 m/s. After the collision, their velocities will be 

1.  10 m/s, 10 rn/s 

2.  15 m/s, 15 m/s

3.  10 rn/s, 15 m/s  

4.  15 m/s, 10 m/s

A mass m with velocity u strikes a wall normally and returns at the same speed. What is the magnitude of the change in momentum of the body when it returns

1.  4 mu

2.  mu

3.  2 mu

4.  0

 A body of mass ${\mathrm{m}}_1$ moving with a velocity $3 {\mathrm{ms}}^{-1}$ collides elastically with another body  at rest of mass ${\mathrm{m}}_2$. After collision the velocities of the two bodies are $2 {\mathrm{ms}}^{-1}$ and $5 {\mathrm{ms}}^{-1}$ respectively along the direction of motion of ${\mathrm{m}}_2$. The ratio $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$ is

1.  $\frac{5}{12}$

2.  $5$

3.  $\frac{1}{5}$

4.  $\frac{12}{5}$

If a body of mass m collides head on, elastically with velocity u with another identical body at rest. After collision velocity of the second body will be

1. zero

2. u

3. 2u

4. data insufficient

The bob A of a simple pendulum is released when the string makes an angle of 45 with the vertical. It hits another bob B of the same material and the same mass kept at rest on a table. If the collision is elastic

1.  Both A and B rise to the same height

2.  Both A and B come to rest at B

3.  Both A and B move with the same velocity of A

4.  A comes to rest and B moves with the velocity of A

A ball hits the floor and rebounds after an inelastic collision. In this case

1.  the momentum of the ball just after the collision is the same as that just before the collision

2.  the mechanical energy of the ball remains the same in the collision

3.  the total momentum of the ball and the earth is conserved

4.  the total energy of the ball and the earth is conserved