A ball is travelling with uniform translatory motion . This means that

Options

A. 1. it is at rest.
B. 2. the path can be a straight line or circular and the ball travels with uniform speed.
C. 3. all parts of the ball have the same velocity (magnitude and direction) and the velocity is constant.
D. 4. the centre of the ball moves with constant velocity and the ball spins about its centre uniformly.

Explanation

To solve the question regarding a ball traveling with uniform translatory motion, we need to analyze the meaning of "uniform translatory motion" and evaluate the given options.

### Step-by-Step Solution:

1. **Understanding Uniform Translatory Motion**:
- Uniform translatory motion refers to the motion of an object where all parts of the object move along the same path and with the same speed. This means that the velocity of the object does not change over time.

2. **Evaluating Each Option**:
- **Option 1: The ball is at rest.**
- This option is incorrect because if the ball is in uniform translatory motion, it must be moving, not at rest.

- **Option 2: The path can be straight or circular and the ball travels with uniform speed.**
- This option is misleading. While the ball can travel with uniform speed, in uniform translatory motion, the path must be straight. A circular path would imply rotational motion, not translatory motion. Therefore, this option is also incorrect.

- **Option 3: All parts of the ball have the same velocity and the velocity is constant.**
- This option is correct. In uniform translatory motion, every part of the ball indeed moves with the same velocity, and since the motion is uniform, this velocity remains constant.

- **Option 4: The center of mass moves with constant velocity and the ball spins about its center uniformly.**
- This option is incorrect because while the center of mass does move with constant velocity, the ball does not spin about its center in uniform translatory motion. The motion is purely translational without any rotation involved.

3. **Conclusion**:
- The only correct statement regarding the ball traveling with uniform translatory motion is **Option 3**: All parts of the ball have the same velocity and the velocity is constant.

### Final Answer:
The correct answer is Option 3.

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