This question was previously asked in

NPCIL Stipendiary Trainee ME 2018

Option 3 : 1.0 m/s

NPCIL 2020 Scientific Assistant Physics Mini Live Test

1344

30 Questions
30 Marks
40 Mins

**Concept:**

When two bodies impact, the Momentum is conserved, i.e.

m1u1 + m2u2 = m1v1 + m2v2

**Calculation:**

**Given:**

m_{1} = 1 kg, m_{2} = 2 kg, u_{1} = 2 m/s, u_{2} = 0, v_{1} = 0, v_{2} = ?

1 × 2 + 0 = 0 + 2 × v_{2}

v_{2} = 1 m/s

__Additional Information__

Properties of different types of collision are given in the table below:

Types of Collision |
Linear momentum |
Total energy |
Kinetic energy |
Coefficient of restitution |

Perfectly elastic collision |
Conserved |
Conserved |
Conserved |
e = 1 |

Inelastic collision |
Conserved |
Conserved |
Not-Conserved |
0 < e < 1 |

Perfectly inelastic collision |
Conserved |
Conserved |
Not-Conserved |
e = 0 |

Perfectly elastic impact

- Momentum is conserved, m1u1 + m2u2 = m1v1 + m2v2
- Kinetic Energy is conserved, \({1\over 2}m_1u_1^2 + {1\over 2}m_2u_2^2 ={1\over 2} m_1v_1^2 + {1\over 2} m_2v_2^2\)
- The two bodies separate after impact
- There is no permanent deformation in the bodies during the impact.
- In a perfectly elastic collision between equal masses of two bodies, velocities exchange on impact.
- Velocity just before impact = Velocity immediately after impact.

Plastic impact

- The two bodies move together with common velocity after the impact
- Moment is conserved, i.e. m1u1 + m2u2 = (m1 + m2) v0
- where v0 is common velocity after impact.
- There is a loss in Kinetic energy after the impact.
- The coefficient of restitution is zero.