If a large number of particles are distributed on `YZ` plane and their centre of mass is at origin of coordinates, then
Sum of moments of masses of all particles about the origin is zero
Sum of momentum of masses of all particles w.r.t. the origin is zero
Sum of moments of masses of all particles about `Y` axis is zero.
Sum of moments of masses of all particles about `Z` axis is zero.

Options

A. Sum of moments of masses of all particles about the origin is zero
B. Sum of momentum of masses of all particles w.r.t. the origin is zero
C. Sum of moments of masses of all particles about `Y` axis is zero.
D. Sum of moments of masses of all particles about `Z` axis is zero.

Answer

To solve the question, we need to analyze the implications of having a large number of particles distributed in the YZ plane with their center of mass at the origin. Let's break down the options one by one.

### Step-by-step Solution:

1. **Understanding the Center of Mass**:
The center of mass (CM) of a system of particles is given by the formula:
\[ \vec{R}_{CM} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + m_3 \vec{r}_3 + \ldots + m_n \vec{r}_n}{m_1 + m_2 + m_3 + \ldots + m_n} \]
Given that the center of mass is at the origin, we have:
\[ m_1 \vec{r}_1 + m_2 \vec{r}_2 + m_3 \vec{r}_3 + \ldots + m_n \vec{r}_n = 0 \]

2. **Option A: Sum of moments of masses about the origin**:
The moment of mass about the origin is given by:
\[ I_{O} = m_1 r_1^2 + m_2 r_2^2 + m_3 r_3^2 + \ldots + m_n r_n^2 \]
Since \( r_i^2 \) (the square of the distance from the origin) is always positive for non-zero masses, the sum cannot be zero. Therefore, **Option A is incorrect**.

3. **Option B: Sum of momentum of masses w.r.t. the origin**:
The total momentum \( \vec{P} \) of the system is given by:
\[ \vec{P} = m_1 \vec{v}_1 + m_2 \vec{v}_2 + m_3 \vec{v}_3 + \ldots + m_n \vec{v}_n \]
If the center of mass is at the origin, the sum of the momenta of the particles must also sum to zero. Therefore, **Option B is correct**.

4. **Option C: Sum of moments of masses about the Y-axis**:
The moment of mass about the Y-axis is given by:
\[ I_{Y} = m_1 z_1^2 + m_2 z_2^2 + m_3 z_3^2 + \ldots + m_n z_n^2 \]
Since \( z_i^2 \) is always positive, the sum cannot be zero. Therefore, **Option C is incorrect**.

5. **Option D: Sum of moments of masses about the Z-axis**:
Similarly, the moment of mass about the Z-axis is given by:
\[ I_{Z} = m_1 y_1^2 + m_2 y_2^2 + m_3 y_3^2 + \ldots + m_n y_n^2 \]
Since \( y_i^2 \) is always positive, the sum cannot be zero. Therefore, **Option D is incorrect**.

### Final Conclusion:
The only correct statement is **Option B**: "Sum of momentum of masses of all particles w.r.t. the origin is zero."