(A) : In a cyclotron the time for one revolution of an ion is independent of its speed or radius of its orbit.
(R) : In a cyclotron the sign of the electric field changes alternately in tune with the circular motion of particle.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the given question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that in a cyclotron, the time for one revolution of an ion is independent of its speed or radius of its orbit.
- In a cyclotron, the time period (T) for one complete revolution is given by the formula:
\[ T = \frac{2\pi m}{qB} \]
where \( m \) is the mass of the particle, \( q \) is the charge of the particle, and \( B \) is the magnetic field strength.
- From this formula, we can see that the time period \( T \) does not depend on the speed \( v \) or the radius \( r \) of the particle's orbit. Thus, the assertion is **true**.

2. **Understanding the Reason (R)**:
- The reason states that in a cyclotron, the sign of the electric field changes alternately in tune with the circular motion of the particle.
- In a cyclotron, the two D-shaped electrodes (D's) are alternately charged to create an electric field that accelerates the ions. As the ions move from one D to the other, the potential alternates, allowing the ions to be accelerated continuously.
- This statement is also **true** as it accurately describes the operation of a cyclotron.

3. **Evaluating the Relationship Between A and R**:
- Although both statements are true, we need to determine if the reason (R) correctly explains the assertion (A).
- The assertion about the independence of the time period from speed and radius is based on the magnetic field and the properties of circular motion, while the reason discusses the alternating electric field which is not directly related to why the time period is independent of speed or radius.
- Therefore, while both statements are true, the reason does not explain the assertion.

### Conclusion:
- The correct answer is that both A and R are true, but R is not the correct explanation of A.