A body of mass 1 kg moving in the x-direction, suddenly explodes into two fragments of mass 1/8 kg and 7/8 kg. An instant later, the smaller fragment is 0.14 m above the x-axis. The position of the heavier fragment is:

Options

A. 1/510 m above x-axis
B. 1/ 50 m below x-axis
C. 7/50 m below x-axis
D. 7/50 m above x-axis

Answer

To solve the problem step by step, we will use the principle of conservation of momentum and the concept of the center of mass.

### Step 1: Understand the initial conditions
Initially, we have a body of mass 1 kg moving in the x-direction. After the explosion, it splits into two fragments:
- Smaller fragment (m1) = 1/8 kg
- Heavier fragment (m2) = 7/8 kg

### Step 2: Analyze the position of the smaller fragment
At a later instant, the smaller fragment (1/8 kg) is located 0.14 m above the x-axis. This means its y-coordinate (y1) is +0.14 m.

### Step 3: Apply the conservation of momentum in the y-direction
Since the body was initially moving only in the x-direction, its initial momentum in the y-direction was zero. Therefore, the total momentum in the y-direction after the explosion must also be zero. This gives us the equation:
\[ m_1 \cdot y_1 + m_2 \cdot y_2 = 0 \]

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
- m1 = 1/8 kg
- y1 = 0.14 m
- m2 = 7/8 kg
- y2 = ? (this is what we need to find)

The equation becomes:
\[ \frac{1}{8} \cdot 0.14 + \frac{7}{8} \cdot y_2 = 0 \]

### Step 5: Solve for y2
Rearranging the equation to solve for y2:
\[ \frac{7}{8} \cdot y_2 = -\frac{1}{8} \cdot 0.14 \]
\[ y_2 = -\frac{0.14}{7} \]

Calculating y2:
\[ y_2 = -0.02 \, \text{m} \]

### Step 6: Interpret the result
The negative sign indicates that the heavier fragment (7/8 kg) is located 0.02 m below the x-axis.

### Conclusion
The position of the heavier fragment is:
\[ y_2 = -0.02 \, \text{m} \]