(A) : The ion cannot move with a speed beyond a certain limit in a cyclotron.
(R) : As velocity increases the mass of ion increases.

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

### Step 1: Analyze the Assertion (A)
The assertion states: "The ion cannot move with a speed beyond a certain limit in a cyclotron."

- In a cyclotron, charged particles (ions) are accelerated in a circular path by a magnetic field. The maximum speed of the ions is determined by the radius of the cyclotron and the magnetic field strength.
- The formula for the maximum velocity \( v_{max} \) of an ion in a cyclotron is given by:
\[ v_{max} = \frac{qBr}{m} \]
where:
- \( q \) = charge of the ion
- \( B \) = magnetic field strength
- \( r \) = radius of the cyclotron
- \( m \) = mass of the ion
- Since this equation shows that the maximum speed is limited by the radius and the mass, the assertion is **true**.

### Step 2: Analyze the Reason (R)
The reason states: "As velocity increases, the mass of the ion increases."

- According to the theory of relativity, as the speed of an object approaches the speed of light, its relativistic mass increases. However, in the context of a cyclotron and typical speeds of ions, we do not consider relativistic effects unless the speeds are a significant fraction of the speed of light.
- In a cyclotron, if the velocity of the ion increases, the mass does not increase in the classical sense. Instead, the relationship between mass and velocity in this context is not directly applicable. Thus, the reason is **false**.

### Conclusion
- The assertion (A) is true.
- The reason (R) is false.
- Therefore, the correct answer is: **A is true and R is false.**

### Final Answer
**Option 3: A is true and R is false.**

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