The axis X and Z in the plane of a disc are mutually perpendicular and Y-axis is perpendicular to the plane of the disc. If the moment of inertia of the body about X and Y axes is respectively 30 kg `m^(2)` and 40 kg `m^(2)` then M.I. about Z-axis in kg `m^(2)` will be:

Options

A. 70
B. 50
C. 10
D. Zero

Answer

To find the moment of inertia about the Z-axis (I_z) of a disc given the moments of inertia about the X-axis (I_x) and Y-axis (I_y), we can use the perpendicular axis theorem.

### Step-by-Step Solution:

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

2. **Identify Given Values**:
From the problem, we have:
- Moment of inertia about the X-axis (I_x) = 30 kg m²
- Moment of inertia about the Y-axis (I_y) = 40 kg m²

3. **Apply the Perpendicular Axis Theorem**:
Substitute the known values into the equation:
\[ I_z = I_x + I_y \]
\[ I_z = 30 \, \text{kg m}^2 + 40 \, \text{kg m}^2 \]

4. **Calculate I_z**:
Perform the addition:
\[ I_z = 30 + 40 = 70 \, \text{kg m}^2 \]

5. **Conclusion**:
The moment of inertia about the Z-axis is:
\[ I_z = 70 \, \text{kg m}^2 \]

### Final Answer:
The moment of inertia about the Z-axis (I_z) is **70 kg m²**.