A body at rest breaks up into \(3\) parts. If \(2\) parts having equal masses fly off perpendicularly each after with a velocity of \(12~\text{m/s}\), then the velocity of the third part which has \(3\) times mass of each part is:

1.	\(4\sqrt{2}~\text{m/s}\) at an angle of \(45^{\circ}\) from each body.
2.	\(24\sqrt{2}~\text{m/s}\) at an angle of \(135^{\circ}\) from each body.
3.	\(6\sqrt{2}~\text{m/s}\) at \(135^{\circ}\) from each body.
4.	\(4\sqrt{2}~\text{m/s}\) at \(135^{\circ}\) from each body.

A particle falls from a height h upon a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled before rebounding has stopped is 

(1) $h\left(\frac{{\displaystyle 1+e^2}}{{\displaystyle 1-e^2}}\right)$

(2) $h\left(\frac{{\displaystyle 1-e^2}}{{\displaystyle 1+e^2}}\right)$

(3) $\frac{h}{2}\left(\frac{{\displaystyle 1-e^2}}{{\displaystyle 1+e^2}}\right)$

(4) $\frac{h}{2}\left(\frac{{\displaystyle 1+e^2}}{{\displaystyle 1-e^2}}\right)$

A body of mass 5 kg moving with a velocity 10m/s collides with another body of the mass 20 kg at, rest and comes to rest. The velocity of the second body due to collision is 

(1) 2.5 m/s

(2) 5 m/s

(3) 7.5 m/s

(4) 10 m/s

A ball of mass m moving with velocity V, makes a head on elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive, velocities of the two balls after collision are-

(1) –V and 2V

(2) 2 V and –V

(3) V and –2V

(4) –2V and V

A spacecraft of mass 'M' and moving with velocity 'v' suddenly breaks in two pieces. After the explosion one of the mass 'm' becomes stationary. What is the velocity of the other part of craft 

(1) $\frac{Mv}{M-m}$

(2) v

(3) $\frac{Mv}{m}$

(4) $\frac{M-m}{m}v$ 

Two masses m_A and m_B moving with velocities v_A and v_B in opposite directions collide elastically. After that the masses m_A and m_B move with velocity v_B and v_A respectively. The ratio (m_A/m_B) is

(1) 1

(2) $\frac{v_A-v_B}{v_A+v_B}$

(3) $(m_A+m_B)/m_A$

(4) $v_A/v_B$ 

A tennis ball is released from height h above ground level. If the ball makes inelastic collision with the ground, to what height will it rise after third collision 

(1) he⁶

(2) e²h

(3) e³h

(4) None of these

A mass \(m\) moves with a velocity \(v\) and collides inelastically with another identical mass. After collision the \(1\)st mass moves with velocity \(\frac{v}{\sqrt{3}}\) in a direction perpendicular to the initial direction of motion. Find the speed of the \(2\)^nd mass after collision: 

1. \(\frac{2}{\sqrt{3}}v\)
2. \(\frac{v}{\sqrt{3}}\)
3. \(v\)
4. \(\sqrt{3} v\)

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is 

1. 90°

2. 0°

3. 45°

4. Different from 90°

A bag (mass \(M\)) hangs by a long thread and a bullet (mass \(m\)) comes horizontally with velocity \(v\) and gets caught in the bag. Then for the combined (bag + bullet) system:
1. \(\text{Momentum is }\frac{mvM}{M+m}\)
2. \(\text{Kinetic energy is }\frac{mv^2}{2}\)
3. \(\text{Momentum is }\frac{mv(M+m)}{M}\)
4. \(\text{Kinetic energy is }\frac{m^2v^2}{2(M+m)}\)