The linear momentum is conserved in

Options

A. elastic collisions
B. inelastic collisions
C. Both a and B
D. Neither a nor b

Explanation

To solve the question regarding the conservation of linear momentum in different types of collisions, we can follow these steps:

### Step 1: Understand the Concept of Linear Momentum
Linear momentum (p) is defined as the product of an object's mass (m) and its velocity (v). Mathematically, it is expressed as:
\[ p = m \cdot v \]

### Step 2: Identify Types of Collisions
There are two main types of collisions:
- **Elastic Collisions**: In these collisions, both momentum and kinetic energy are conserved.
- **Inelastic Collisions**: In these collisions, momentum is conserved, but kinetic energy is not.

### Step 3: Apply the Law of Conservation of Momentum
The law of conservation of momentum states that in a closed system (where no external forces are acting), the total momentum before the collision is equal to the total momentum after the collision. This applies to both types of collisions:
- For elastic collisions:
\[ p_{\text{initial}} = p_{\text{final}} \]
- For inelastic collisions:
\[ p_{\text{initial}} = p_{\text{final}} \]

### Step 4: Analyze the Options
Given the options:
1. Elastic collisions
2. Inelastic collisions
3. Both A and B
4. Neither A nor B

Since we have established that linear momentum is conserved in both elastic and inelastic collisions, we can conclude that:

### Step 5: Choose the Correct Option
The correct answer is:
**Both A and B (Option 3)**

### Summary
Linear momentum is conserved in both elastic and inelastic collisions.

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