Assertion: A charged particle enters in a magnetic field `B=B_0hati with velocity v=v_0hati+v_0hatj, ` then minimum speed of charged particle may be `v_0`.
Reason: A variable acceleration particle may be `v_0`.

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 1: Analyze the Assertion
The assertion states that a charged particle enters a magnetic field with a velocity \( \vec{v} = v_0 \hat{i} + v_0 \hat{j} \) and the minimum speed of the charged particle may be \( v_0 \).

1. **Calculate the Magnitude of Velocity**:
The magnitude of the velocity \( \vec{v} \) can be calculated using the Pythagorean theorem:
\[ |\vec{v}| = \sqrt{(v_0)^2 + (v_0)^2} = \sqrt{2v_0^2} = v_0 \sqrt{2} \]
This shows that the speed of the particle is \( v_0 \sqrt{2} \), which is greater than \( v_0 \).

2. **Conclusion about Assertion**:
Since the minimum speed of the charged particle cannot be \( v_0 \) (it is actually \( v_0 \sqrt{2} \)), the assertion is **false**.

### Step 2: Analyze the Reason
The reason states that a variable acceleration particle may be \( v_0 \).

1. **Understanding Variable Acceleration**:
A charged particle moving in a magnetic field experiences a centripetal force that changes the direction of its velocity, leading to variable acceleration. The speed of the particle remains constant, but the direction changes, resulting in variable acceleration.

2. **Conclusion about Reason**:
The statement that a variable acceleration particle may have a speed of \( v_0 \) is **true** because the particle can indeed have a constant speed while experiencing variable acceleration due to the change in direction.

### Final Conclusion
- The assertion is **false**.
- The reason is **true**.

### Summary of the Solution
- Assertion: False (minimum speed is \( v_0 \sqrt{2} \)).
- Reason: True (a charged particle can have constant speed while experiencing variable acceleration).