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 1: Understand 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 (Y-axis) is equal to the sum of the moments of inertia about two perpendicular axes (X and Z axes) lying in that plane.

### Step 2: Define the Axes
In this scenario:
- The body is in the X-Z plane.
- The axes are defined as follows:
- X-axis: along the horizontal direction.
- Z-axis: along the depth direction.
- Y-axis: perpendicular to the X-Z plane.

### Step 3: Apply the Theorem
According to the theorem:
\[ I_Y = I_X + I_Z \]
Where:
- \( I_Y \) is the moment of inertia about the Y-axis.
- \( I_X \) is the moment of inertia about the X-axis.
- \( I_Z \) is the moment of inertia about the Z-axis.

### Step 4: Conclusion
Thus, if a body is in the X-Z plane, the moment of inertia about the Y-axis can be calculated as the sum of the moments of inertia about the X and Z axes.

### Final Answer
The correct statement according to the theorem of perpendicular axes is:
\[ I_Y = I_X + I_Z \]