By the theorem of perpendicular axes, if a body be in X-Z-plane then :-

Options

A. `I_(x)-I_(y)=I_(z)`
B. `I_(x)+I_(z)=I_(y)`
C. `I_(x)+I_(y)=I_(z)`
D. `I_(y)+I_(z)=I_(x)`

Answer

To solve the problem using the theorem of perpendicular axes, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Theorem of Perpendicular Axes**:
- The theorem states that for a planar body lying in the X-Z plane, the moment of inertia about an axis perpendicular to the plane (Z-axis) is equal to the sum of the moments of inertia about the two axes lying in the plane (X and Y axes).
- Mathematically, this can be expressed as:
\[ I_z = I_x + I_y \]
where \(I_z\) is the moment of inertia about the Z-axis, \(I_x\) is the moment of inertia about the X-axis, and \(I_y\) is the moment of inertia about the Y-axis.

2. **Identifying the Axes**:
- In this case, we have a body in the X-Z plane, meaning that the Y-axis is perpendicular to the plane formed by the X and Z axes.

3. **Applying the Theorem**:
- According to the theorem, we can write:
\[ I_z = I_x + I_y \]
- This indicates that if we know the moments of inertia about the X and Y axes, we can find the moment of inertia about the Z-axis.

4. **Conclusion**:
- Therefore, the correct relationship according to the theorem of perpendicular axes is:
\[ I_x + I_y = I_z \]
- This means that the moment of inertia about the Z-axis is equal to the sum of the moments of inertia about the X and Y axes.

### Final Answer:
The correct statement according to the theorem of perpendicular axes for a body in the X-Z plane is:
\[ I_x + I_y = I_z \]