When two marbles collide, their total momentum before collision is equal to

Options

A. the difference in their momentum after collision.
B. the average of their momentum after collision.
C. the square of the sum of their momentum after collision.
D. their total momentum after collision.

Explanation

To solve the question "When two marbles collide, their total momentum before collision is equal to...", we can follow these steps:

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

### Step 2: Define total momentum before the collision
When two marbles collide, we need to consider the momentum of both marbles before the collision. If we denote the mass and velocity of the first marble as \( m_1 \) and \( v_1 \), and for the second marble as \( m_2 \) and \( v_2 \), the total momentum before the collision (denoted as \( P_i \)) can be expressed as:
\[ P_i = m_1 \times v_1 + m_2 \times v_2 \]

### Step 3: Apply the law of conservation of momentum
According to the law of conservation of momentum, the total momentum of a closed system before an event (like a collision) is equal to the total momentum after the event. This means:
\[ P_i = P_f \]
where \( P_f \) is the total momentum after the collision.

### Step 4: Conclusion
Thus, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the answer to the question is that the total momentum before the collision is equal to the total momentum after the collision.

### Final Answer
The total momentum before the collision is equal to the total momentum after the collision.

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