The theorem of perpendicular axes is not applicable for determination of moment of inertia along the diameter, for which of the following body :-

Options

A. sphere
B. disc
C. ring
D. blade

Answer

To determine which body the theorem of perpendicular axes is not applicable for when calculating the moment of inertia along the diameter, we need to analyze the options provided: sphere, disc, ring, and blade.

### Step-by-Step Solution:

1. **Understanding the Perpendicular Axis Theorem**:
The perpendicular axis theorem states that for a planar body lying in the XY-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 two perpendicular axes (X and Y) lying in the plane.
\[ I_Z = I_X + I_Y \]

2. **Analyzing the Sphere**:
A sphere is a three-dimensional body and is symmetrical about all axes. The moment of inertia for a sphere is the same regardless of the axis chosen. Thus, the perpendicular axis theorem does not apply since it is not a planar body.

3. **Analyzing the Disc**:
A disc is a planar body. The moment of inertia about its diameter (X or Y-axis) can be calculated using the perpendicular axis theorem. Therefore, the theorem is applicable here.

4. **Analyzing the Ring**:
A ring is also a planar body. The moment of inertia about its diameter can also be calculated using the perpendicular axis theorem. Hence, it is applicable.

5. **Analyzing the Blade**:
A blade can be considered a planar body as well, and the perpendicular axis theorem can be applied to find the moment of inertia about its diameter.

6. **Conclusion**:
Since the perpendicular axis theorem is not applicable for three-dimensional bodies, the correct answer is the sphere (Option A).

### Final Answer:
The theorem of perpendicular axes is not applicable for the determination of moment of inertia along the diameter for the sphere (Option A).

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