The perpendicular axes theorem is applicable only for the axes passing through the center of mass of the body. Is it true or false??

Answer

To determine whether the statement "The perpendicular axes theorem is applicable only for the axes passing through the center of mass of the body" is true or false, we can analyze the conditions under which the perpendicular axes theorem is valid.

### Step-by-Step Solution:

1. **Understanding the Perpendicular Axes Theorem**:
The perpendicular axes theorem states that for a planar object (a two-dimensional shape), the moment of inertia about an axis perpendicular to the plane (let's say the z-axis) is equal to the sum of the moments of inertia about two mutually perpendicular axes (the x-axis and y-axis) lying in the plane of the object. Mathematically, this can be expressed as:
\[ I_z = I_x + I_y \]
where \(I_z\) is the moment of inertia about the z-axis, and \(I_x\) and \(I_y\) are the moments of inertia about the x-axis and y-axis, respectively.

2. **Conditions for the Theorem**:
- The object must be planar (2D).
- The axes must be mutually perpendicular.
- The theorem does not require that the axes pass through the center of mass of the object.

3. **Analyzing the Statement**:
The statement claims that the theorem is applicable only for axes that pass through the center of mass. However, this is not true. The theorem can be applied to any two mutually perpendicular axes in the plane of the object, regardless of whether they pass through the center of mass or not.

4. **Conclusion**:
Since the perpendicular axes theorem does not impose the condition that the axes must pass through the center of mass, the statement is **False**.

### Final Answer:
The statement is **False**.