A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together shifts horizontally towards

Options

A. heavier piece
B. lighter piece
C. does not shift horizontally
D. depends on the verical velocity at the tiem of breaking

Answer

To solve the problem of how the center of mass of two parts of unequal masses shifts horizontally when a body falling vertically under gravity breaks apart, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the System**: We have a body falling vertically under the influence of gravity. When it breaks into two parts of unequal masses, we need to analyze the behavior of the center of mass of these two parts.

2. **Consider Forces Acting on the System**: Since the body is falling vertically, the only force acting on it is gravity, which acts downwards. Importantly, there are no external forces acting in the horizontal direction.

3. **Apply the Center of Mass Formula**: The center of mass (CM) of a system of particles is given by the formula:
\[ \text{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
where \(m_1\) and \(m_2\) are the masses of the two parts, and \(x_1\) and \(x_2\) are their respective positions.

4. **Analyze the Horizontal Motion**: Since there are no external forces in the horizontal direction, the horizontal acceleration of the center of mass is zero. This means that the center of mass does not have any horizontal velocity.

5. **Conclusion on Horizontal Shift**: Because the center of mass does not have any horizontal velocity and there are no external forces acting in the horizontal direction, the center of mass does not shift horizontally. It remains in the same horizontal position as it was before the body broke apart.

6. **Final Answer**: Therefore, the center of mass of the two parts taken together does not shift horizontally.