It is not possible to determine precisely both the position and momentum (or velocity) of a small moving particle such as electron, proton etc. This is known as Heisenberg uncertainty principle. The mathematical form of this principle is :
`Delta x.Delta p ge (h)/(4pi)` (constant)
However this principle is irrelevant in case of bigger particles such as a cup, ball, car etc., that we come across in our daily life.
In case of small microscopic particles, Heisenberg's uncertainty principle rules out simultaneous exact determination of their

Options

A. energy and velocity
B. charge density and radius
C. postion and momentum
D. none of the above three

Explanation

To solve the question regarding the Heisenberg uncertainty principle, we will break down the information provided and arrive at the correct conclusion step by step.

### Step-by-Step Solution:

1. **Understanding the Heisenberg Uncertainty Principle**:
- The Heisenberg uncertainty principle states that it is impossible to simultaneously know both the position (Δx) and momentum (Δp) of a particle with absolute precision. The more accurately one of these properties is known, the less accurately the other can be known.

2. **Mathematical Representation**:
- The principle is mathematically expressed as:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
- Here, Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is Planck's constant.

3. **Application to Small Particles**:
- This principle is particularly relevant for small particles such as electrons and protons, where the uncertainties in their measurements become significant due to their small mass and size.

4. **Irrelevance for Larger Objects**:
- For larger objects like cups, balls, or cars, the uncertainties in position and momentum are negligible, making the principle practically irrelevant in everyday situations.

5. **Conclusion**:
- The question asks what the Heisenberg uncertainty principle rules out in terms of simultaneous exact determination. The answer is that it rules out the simultaneous exact determination of both the position and momentum of small particles.

### Final Answer:
The Heisenberg uncertainty principle rules out the simultaneous exact determination of the **position and momentum** of small moving particles such as electrons and protons.

---