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) for the disc, we can use the perpendicular axis theorem. According to this theorem, for a planar body, 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 mutually perpendicular axes lying in the plane (X-axis and Y-axis).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Moment of inertia about the X-axis (I_x) = 30 kg m²
- Moment of inertia about the Y-axis (I_y) = 40 kg m²

2. **Apply the Perpendicular Axis Theorem:**
The theorem states:
\[ I_z = I_x + I_y \]
where:
- \(I_z\) is the moment of inertia about the Z-axis,
- \(I_x\) is the moment of inertia about the X-axis,
- \(I_y\) is the moment of inertia about the Y-axis.

3. **Substitute the Known Values:**
\[ I_z = 30 \, \text{kg m}^2 + 40 \, \text{kg m}^2 \]

4. **Calculate I_z:**
\[ I_z = 70 \, \text{kg m}^2 \]

### Final Answer:
The moment of inertia about the Z-axis is \(70 \, \text{kg m}^2\).

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