The moment of inertia of a rod about an axis through its centre and perpendicular to it, is `(1)/(12)ML^(2)` (where, M is the mass and L is length of the rod). The rod is bent in the middle, so that two halves make an angle of `60^(@)`. The moment of inertia of the bent rod about the same axis would be

Explanation

To find the moment of inertia of a bent rod about the same axis after bending it at an angle of \(60^\circ\), we can follow these steps:

### Step 1: Understand the Initial Moment of Inertia
The moment of inertia \(I\) of a straight rod of mass \(M\) and length \(L\) about an axis through its center and perpendicular to it is given by:
\[ I = \frac{1}{12} ML^2 \]

### Step 2: Analyze the Bending of the Rod
When the rod is bent in the middle, it forms two halves, each with a mass of \(\frac{M}{2}\) and a length of \(\frac{L}{2}\). The two halves make an angle of \(60^\circ\) with respect to each other.

### Step 3: Calculate the Moment of Inertia for Each Half
The moment of inertia of a rod about one of its ends is given by:
\[ I_{\text{end}} = \frac{1}{3} m L^2 \]
For each half of the rod:
- Mass \(m = \frac{M}{2}\)
- Length \(L = \frac{L}{2}\)

Substituting these values into the formula:
\[ I_1 = \frac{1}{3} \left(\frac{M}{2}\right) \left(\frac{L}{2}\right)^2 = \frac{1}{3} \left(\frac{M}{2}\right) \left(\frac{L^2}{4}\right) = \frac{ML^2}{24} \]

### Step 4: Calculate the Moment of Inertia for the Second Half
Since the second half of the rod is also identical to the first half, it will have the same moment of inertia:
\[ I_2 = \frac{ML^2}{24} \]

### Step 5: Combine the Moments of Inertia
The total moment of inertia of the bent rod about the same axis is the sum of the moments of inertia of both halves:
\[ I_{\text{total}} = I_1 + I_2 = \frac{ML^2}{24} + \frac{ML^2}{24} = \frac{2ML^2}{24} = \frac{ML^2}{12} \]

### Conclusion
Thus, the moment of inertia of the bent rod about the same axis remains:
\[ I = \frac{ML^2}{12} \]