Assertion When a charged particle moves perpendicular to a uniform magnetic field then its momentum remains constant.
Reason Magnetic force acts perpendicular to the velocity of the particle.

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 question regarding the assertion and reason provided, we will analyze both statements step by step.

### Step 1: Understanding the Assertion
The assertion states that "when a charged particle moves perpendicular to a uniform magnetic field, then its momentum remains constant."

**Hint:** Consider the definition of momentum and how it is affected by forces acting on the particle.

### Step 2: Analyzing the Motion of the Charged Particle
When a charged particle moves in a magnetic field, it experiences a magnetic force (Lorentz force) given by the equation:
\[ F = Q(v \times B) \]
where:
- \( F \) is the magnetic force,
- \( Q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field.

Since the particle is moving perpendicular to the magnetic field, the angle between the velocity and the magnetic field is 90 degrees.

**Hint:** Recall that the sine of 90 degrees is 1, which simplifies the force equation.

### Step 3: Evaluating the Force
The magnitude of the magnetic force when the particle moves perpendicular to the magnetic field is:
\[ F = QvB \]
This force acts perpendicular to the velocity of the particle.

**Hint:** Think about how a force acting perpendicular to the direction of motion affects the speed and direction of the particle.

### Step 4: Understanding Momentum
Momentum \( P \) is defined as:
\[ P = mv \]
where \( m \) is the mass of the particle and \( v \) is its velocity. For momentum to remain constant, the net force acting on the particle must be zero (from Newton's second law).

**Hint:** Consider the implications of a non-zero force on the momentum of the particle.

### Step 5: Conclusion on the Assertion
Since the magnetic force is acting on the particle, it causes a change in the direction of the velocity, which means the momentum is changing. Therefore, the assertion that the momentum remains constant is **false**.

### Step 6: Understanding the Reason
The reason states that "magnetic force acts perpendicular to the velocity of the particle." This is indeed true, as established in our earlier analysis.

**Hint:** Revisit the definition of the Lorentz force and how it relates to the motion of charged particles in a magnetic field.

### Final Conclusion
- **Assertion:** False (momentum does not remain constant due to the magnetic force).
- **Reason:** True (the magnetic force is indeed perpendicular to the velocity).

Thus, the correct answer to the question is that the assertion is false and the reason is true.