Which of the following is not a derived force?

Options

A. Tension in a string
B. van der Waal force
C. Nuclear force between proton-proton
D. Electrostatic force between proton-proton

Answer

To determine which of the following forces is not a derived force, we need to understand the concept of derived forces. Derived forces are those that can be calculated or expressed mathematically based on fundamental principles.

### Step-by-Step Solution:

1. **Define Derived Forces**: Derived forces are forces that can be calculated using mathematical formulas or principles. They are typically based on fundamental forces and can be expressed in terms of other physical quantities.

2. **Analyze the Options**:
- **Option A: Tension in a String**: Tension can be calculated using Newton's laws and can be expressed mathematically. Therefore, it is a derived force.
- **Option B: Van der Waals Forces**: Although calculating Van der Waals forces can be complex, they can still be derived using principles of intermolecular forces. Thus, this is also a derived force.
- **Option C: Nuclear Force between Protons**: The nuclear force is a fundamental interaction that is not easily expressed mathematically in a simple form. It is a strong force that holds protons and neutrons together in the nucleus and cannot be derived in the same way as the other forces mentioned.
- **Option D: Electrostatic Force between Protons**: This force can be calculated using Coulomb's law, which is a mathematical expression. Hence, it is a derived force.

3. **Conclusion**: Based on the analysis, the nuclear force between protons (Option C) is not a derived force because it cannot be easily expressed mathematically like the other forces.

### Final Answer:
**The nuclear force between protons is not a derived force.**

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