Assertion: A charged particle is moving in a circle with constant speed in uniform magnetic field. If we increase the speed of particle to twice, its acceleration will become four times.
Reason: In circular path of radius `R` with constant speed `v`, acceleration is given by `v^2/R`

Options

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

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if a charged particle moving in a circular path with constant speed in a uniform magnetic field has its speed increased to twice its original speed, its acceleration will become four times the original acceleration.

2. **Centripetal Acceleration Formula**:
- The centripetal acceleration \( a \) of an object moving in a circular path of radius \( R \) with speed \( v \) is given by the formula:
\[ a = \frac{v^2}{R} \]

3. **Calculating Initial Acceleration**:
- Let’s denote the initial speed of the particle as \( v \). The initial acceleration \( a_1 \) can be expressed as:
\[ a_1 = \frac{v^2}{R} \]

4. **Calculating Acceleration at Double Speed**:
- If the speed is increased to \( 2v \), the new acceleration \( a_2 \) will be:
\[ a_2 = \frac{(2v)^2}{R} = \frac{4v^2}{R} \]

5. **Comparing Accelerations**:
- Now, comparing \( a_2 \) with \( a_1 \):
\[ a_2 = 4 \left(\frac{v^2}{R}\right) = 4a_1 \]
- This shows that the new acceleration \( a_2 \) is indeed four times the original acceleration \( a_1 \).

6. **Conclusion on Assertion**:
- The assertion is **true** because when the speed is doubled, the acceleration becomes four times the original acceleration.

7. **Understanding the Reason**:
- The reason states that in a circular path of radius \( R \) with constant speed \( v \), the acceleration is given by \( \frac{v^2}{R} \).
- This statement is also **true** as it correctly describes the formula for centripetal acceleration.

8. **Final Evaluation**:
- Since both the assertion and the reason are true, but the assertion claims an incorrect relationship regarding the change in acceleration, we conclude that:
- The assertion is **false**.
- The reason is **true**.

### Final Answer:
- Assertion: False
- Reason: True