An explosion in a rigid pipe shoots out three pieces. A 6 g piece comes out the right end. A 4 g piece comes out the left end with twice the speed of the 6 g piece. From which end does the third piece emerge?

A. B. C
Right end Left end Not enough information to answer this question

To determine the end from which the third piece emerges, we need to understand the principles of conservation of momentum.

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces are acting on it. In this case, the system consists of the three pieces of the pipe.

Let's analyze the situation:

1. An explosion occurs, so the system is not isolated from external forces. However, we can assume that the explosion happens instantaneously, and no external forces act on the pieces afterwards.

2. The first piece, weighing 6 g, comes out of the right end. The momentum of this piece can be calculated by multiplying its mass (6 g) by its velocity (let's call it v1).

3. The second piece, weighing 4 g, comes out of the left end with twice the speed of the first piece. Therefore, its velocity is 2v1. Using the same logic as before, we can calculate the momentum of this piece by multiplying its mass (4 g) by its velocity (2v1).

4. Now, let's consider the third piece, which we need to determine the emergence end. We know that the system's total momentum must be conserved, so the sum of the momentum of the first and second piece must be equal to the momentum of the third piece.

5. Since we haven't been given any specific information about the third piece, we can assume it weighs m g and has a velocity of v3. Therefore, the momentum of the third piece is given by m * v3.

6. Equating the momentum of the first plus the momentum of the second piece to the momentum of the third piece, we have:
6g * v1 + 4g * 2v1 = m * v3

7. Simplifying the equation, we get:
6v1 + 8v1 = m * v3
14v1 = m * v3

At this point, we can see that to determine from which end the third piece emerges, we need either the value of m or the ratio between v1 and v3. Since we haven't been provided with that information, we cannot conclusively answer the question.

Therefore, the answer is: Not enough information to answer this question (C).