Identify the correct statement among the following.

Options

A. cyclotron frequency is dependent on speed of the charged particle
B. kinetic energy of charged particle in cyclotron does not dependent on its mass
C. cyclotron frequency does not depend on the speed of the charged particle
D. kinetic energy of charged particle in cyclotron is independent of its charge

Answer

To solve the question, we need to analyze the four statements provided and determine which one is correct regarding cyclotron frequency and kinetic energy of charged particles.

### Step-by-Step Solution:

1. **Understanding Cyclotron Frequency**:
- Cyclotron frequency (f) is defined as the frequency at which a charged particle orbits in a magnetic field. It can be expressed mathematically as:
\[ f = \frac{qB}{2\pi m} \]
where \( q \) is the charge of the particle, \( B \) is the magnetic field strength, and \( m \) is the mass of the particle.

2. **Analyzing the Statements**:
- **Option 1**: "The cyclotron frequency is dependent on the speed of a charged particle."
- This statement is **incorrect** because cyclotron frequency does not depend on the speed of the particle; it depends on the charge, magnetic field, and mass.

- **Option 2**: "The kinetic energy of a charged particle in cyclotron does not depend on its mass."
- Kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
- This statement is **incorrect** as kinetic energy does depend on mass.

- **Option 3**: "Cyclotron frequency does not depend on the speed of the charged particle."
- This statement is **correct**. As derived, cyclotron frequency is independent of the speed of the charged particle.

- **Option 4**: "Kinetic energy of a charged particle in cyclotron is independent of its charge."
- This statement is **incorrect** because kinetic energy is influenced by the charge of the particle.

3. **Conclusion**:
- The only correct statement among the options is **Option 3**: "Cyclotron frequency does not depend on the speed of the charged particle."

### Final Answer:
The correct statement is: **Cyclotron frequency does not depend on the speed of the charged particle.** (Option 3)