Assertion A ball tied by thread is undergoing circular motion (of radius R) in a vertical plane. (Thread always remains in vertical plane). The difference of maximum and minimum tension in thread is independent of speed (u) of ball at the lowest position `(ugtsqrt(5gR))`.
Reason For a ball of mass m tied by thread undergoing vertical circular motion (of radius R), difference in maximum and minimum magnitude of centripetal aceleraion of the ball is independent of speed (u) of ball at the lowest position `(ugrsqrt5gR))`.

Options

A. (a)Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the given problem, we need to analyze the assertion and reason provided, focusing on the tension in the thread and the centripetal acceleration of the ball undergoing circular motion.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a ball of mass \( m \) tied to a thread, undergoing vertical circular motion with radius \( R \).
- The ball has a speed \( u \) at the lowest point of the circular path.

2. **Identifying Forces**:
- At the lowest point (point B), the forces acting on the ball are:
- Tension \( T_B \) acting upwards.
- Weight \( mg \) acting downwards.
- At the highest point (point A), the forces are:
- Tension \( T_A \) acting downwards.
- Weight \( mg \) also acting downwards.

3. **Applying Newton's Second Law**:
- At the lowest point (point B):
\[ T_B - mg = \frac{m u^2}{R} \]
Rearranging gives:
\[ T_B = \frac{m u^2}{R} + mg \quad \text{(Equation 1)} \]

- At the highest point (point A):
\[ T_A + mg = \frac{m v^2}{R} \]
Rearranging gives:
\[ T_A = \frac{m v^2}{R} - mg \quad \text{(Equation 2)} \]

4. **Using Conservation of Energy**:
- The mechanical energy at the lowest point is equal to the mechanical energy at the highest point:
\[ \frac{1}{2} m u^2 = \frac{1}{2} m v^2 + mg(2R) \]
- Rearranging gives:
\[ u^2 - v^2 = 4gR \quad \text{(Equation 3)} \]

5. **Finding the Difference in Tension**:
- The difference in tension \( \Delta T \) is given by:
\[ \Delta T = T_B - T_A \]
- Substituting Equations 1 and 2 into this:
\[ \Delta T = \left(\frac{m u^2}{R} + mg\right) - \left(\frac{m v^2}{R} - mg\right) \]
- Simplifying this gives:
\[ \Delta T = \frac{m u^2}{R} + mg - \frac{m v^2}{R} + mg = \frac{m (u^2 - v^2)}{R} + 2mg \]
- Using Equation 3:
\[ \Delta T = \frac{m (4gR)}{R} + 2mg = 4mg + 2mg = 6mg \]

6. **Conclusion**:
- The difference in tension \( \Delta T = 6mg \) is independent of the speed \( u \) at the lowest position.
- Therefore, the assertion is true.

7. **Analyzing the Reason**:
- The reason states that the difference in maximum and minimum centripetal acceleration is independent of speed \( u \).
- The centripetal acceleration at the lowest point is \( \frac{u^2}{R} \) and at the highest point is \( \frac{v^2}{R} \).
- The difference in centripetal acceleration is:
\[ \Delta a_c = \frac{u^2 - v^2}{R} = \frac{4gR}{R} = 4g \]
- This difference is also independent of \( u \).

### Final Answer:
Both the assertion and reason are true, and the reason correctly explains the assertion.