For of particles under central forcer field, the total angular momentum is conserved.
The torque acting on such a system is 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 the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false

Explanation

To solve the question regarding the conservation of angular momentum for a particle under a central force field, we will analyze the assertion and the reason provided in the statement.

### Step-by-Step Solution:

1. **Understanding Central Force**:
A central force is a force that acts along the line connecting the particle and a fixed point (the center). Examples include gravitational and electrostatic forces.

2. **Torque in Central Force Fields**:
The torque (\( \tau \)) acting on a particle due to a central force is given by the equation:
\[ \tau = \vec{r} \times \vec{F} \]
where \( \vec{r} \) is the position vector from the center to the particle and \( \vec{F} \) is the force vector. For a central force, \( \vec{F} \) is directed along \( \vec{r} \), making the angle between \( \vec{r} \) and \( \vec{F} \) equal to 0 degrees.

3. **Calculating Torque**:
Since the angle between \( \vec{r} \) and \( \vec{F} \) is 0 degrees, the sine of the angle is zero:
\[ \tau = rF \sin(0) = 0 \]
Therefore, the torque acting on the system is zero.

4. **Conservation of Angular Momentum**:
The angular momentum (\( \vec{L} \)) of a particle is defined as:
\[ \vec{L} = \vec{r} \times \vec{p} \]
where \( \vec{p} \) is the linear momentum. The rate of change of angular momentum is equal to the torque:
\[ \frac{d\vec{L}}{dt} = \tau \]
Since we have established that \( \tau = 0 \), it follows that:
\[ \frac{d\vec{L}}{dt} = 0 \implies \vec{L} = \text{constant} \]
This indicates that angular momentum is conserved.

5. **Conclusion**:
Both the assertion that "the total angular momentum is conserved" and the reason that "the torque acting on such a system is zero" are true. Moreover, the reason correctly explains the assertion.

### Final Answer:
The correct option is **a**: Both assertion and reason are true, and the reason is the correct explanation of the assertion.