(A) : The frequency of charge circulating in cyclotron depend upon the speed of the charge.
(R) : The time which charge spends inside a dee of cyclotron is dependent on its velocity and radius of the semicircular path.

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 problem, we need to analyze both the assertion and the reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "The frequency of charge circulating in a cyclotron depends upon the speed of the charge."
- In a cyclotron, the frequency (f) of a charged particle moving in a magnetic field is given by the formula:
\[ f = \frac{qB}{2\pi m} \]
where:
- \( q \) = charge of the particle
- \( B \) = magnetic field strength
- \( m \) = mass of the particle
- From this formula, we can see that the frequency does not depend on the speed (velocity) of the charge. Therefore, the assertion is **false**.

2. **Understanding the Reason (R)**:
- The reason states that "The time which charge spends inside a dee of cyclotron is dependent on its velocity and radius of the semicircular path."
- The time period (T) for a charged particle in a cyclotron is given by:
\[ T = \frac{2\pi m}{qB} \]
- Again, we observe that this formula does not include the velocity or the radius of the semicircular path. Thus, the time spent inside a dee is also **independent** of both velocity and radius. Therefore, the reason is also **false**.

3. **Conclusion**:
- Since both the assertion and the reason are false, we conclude that neither statement is correct.

### Final Answer:
Both the assertion (A) and the reason (R) are false.