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 the center of mass of a body that falls vertically downwards and breaks into two parts of unequal masses, we can follow these steps:

### Step 1: Understand the System
We have a single body falling under the influence of gravity. When it breaks into two parts, we need to analyze the motion of these parts in terms of their masses and the forces acting on them.

### Step 2: Identify Forces
Since the body is falling vertically, the only force acting on it is gravity, which acts downwards. There are no horizontal forces acting on the body before or after it breaks apart.

### Step 3: Analyze the Center of Mass
The center of mass (CM) of a system is influenced by the distribution of mass and the forces acting on it. In this case, since there are no external forces acting in the horizontal direction, the horizontal position of the center of mass will remain unchanged.

### Step 4: Consider the Breaking of the Body
When the body breaks into two parts, the internal forces (the forces that cause the body to break) do not affect the overall horizontal motion of the center of mass. The center of mass will only shift if there are external forces acting on the system.

### Step 5: Conclusion
Since there are no external forces acting horizontally on the system, the center of mass of the two parts taken together does not shift horizontally. It remains in the same horizontal position as it was before the body broke apart.

### Final Answer
The center of mass of the two parts taken together does not shift horizontally.

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