In an inelastic collision (a) momentum of the system is always conserved (b) velocity of separation is less than the velocity of approach. (c) the coefficient of restitution can be zero. (d) All of the above

Options

A. (a) momentum of the system is always conserved
B. (b) velocity of separation is less than the velocity of approach.
C. (c) the coefficient of restitution can be zero
D. (d) All of the above

Answer

To solve the question regarding inelastic collisions and determine which statements are correct, let's analyze each statement step by step.

### Step 1: Understanding Inelastic Collisions
Inelastic collisions are defined as collisions where kinetic energy is not conserved, but momentum is conserved. This means that some kinetic energy is transformed into other forms of energy (like heat or sound) during the collision.

### Step 2: Analyzing Statement (a)
**Statement (a):** "Momentum of the system is always conserved."
- In an inelastic collision, the total momentum before the collision equals the total momentum after the collision. Therefore, this statement is **true**.

### Step 3: Analyzing Statement (b)
**Statement (b):** "Velocity of separation is less than the velocity of approach."
- The coefficient of restitution (e) is defined as the ratio of the relative velocity of separation to the relative velocity of approach. For inelastic collisions, this coefficient can be less than 1, and in some cases, it can be 0. Hence, the velocity of separation is indeed less than the velocity of approach. This statement is also **true**.

### Step 4: Analyzing Statement (c)
**Statement (c):** "The coefficient of restitution can be zero."
- The coefficient of restitution can be zero in perfectly inelastic collisions, where the two colliding bodies stick together after the collision. Therefore, this statement is also **true**.

### Step 5: Conclusion
Since all three statements (a), (b), and (c) are true, the correct answer is:
**(d) All of the above.**

### Final Answer:
The correct option is **(d) All of the above.**

---