Assertion In a uniform magnetic field `B=B_(0)hat(k)`, if velocity of a charged particle is `v_(0)hat(i)` at t = 0, then it can have the velocity `v_(0)hat(j)` at some other instant.
Reason In uniform magnetic field, acceleration of a charged particle is always zero.

Options

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

Answer

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

### Step 1: Understand the Assertion
The assertion states that in a uniform magnetic field \( \mathbf{B} = B_0 \hat{k} \), if the velocity of a charged particle is \( \mathbf{v} = v_0 \hat{i} \) at \( t = 0 \), then it can have the velocity \( \mathbf{v} = v_0 \hat{j} \) at some other instant.

**Analysis**: In a uniform magnetic field, the magnetic force acts perpendicular to both the velocity of the charged particle and the magnetic field direction. This means that the magnetic force can change the direction of the velocity but not its magnitude. Therefore, if the particle starts with a velocity in the \( \hat{i} \) direction, it cannot spontaneously change to a velocity in the \( \hat{j} \) direction without an external force acting on it. Thus, the assertion is **false**.

### Step 2: Understand the Reason
The reason states that in a uniform magnetic field, the acceleration of a charged particle is always zero.

**Analysis**: This statement is not entirely accurate. While it is true that in a uniform magnetic field, the magnetic force does not do work on the charged particle (since the force is always perpendicular to the displacement), the particle can still experience centripetal acceleration if it moves in a circular path due to the magnetic force. However, if we consider the net force acting on the particle, it can be zero if the particle moves with constant velocity. Therefore, the reason is **true** in the context that the net acceleration in the direction of motion is zero, but it can have centripetal acceleration if it is moving in a circular path.

### Conclusion
- **Assertion**: False
- **Reason**: True

### Final Answer
The assertion is false, but the reason is true.

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