Moment of inertia of a bar magnet of mass `M`,length `L` and breadth `B` is `I`. Then moment of inertia of another bar magnet with all these values doubled would be

Options

A. `8I`
B. `4I`
C. `2I`
D. `I`

Explanation

To find the moment of inertia of a bar magnet when its mass, length, and breadth are all doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Moment of Inertia Formula**:
The moment of inertia \( I \) of a bar about its center of mass is given by the formula:
\[ I = \frac{ML^2}{12} \]
where \( M \) is the mass and \( L \) is the length of the bar.

2. **Identify Initial Values**:
We are given:
- Mass of the first bar magnet: \( M \)
- Length of the first bar magnet: \( L \)
- Breadth of the first bar magnet: \( B \) (not needed for this calculation)

Therefore, the moment of inertia \( I \) of the first bar magnet is:
\[ I = \frac{ML^2}{12} \]

3. **Determine New Values**:
For the second bar magnet, all values are doubled:
- New mass: \( 2M \)
- New length: \( 2L \)
- New breadth: \( 2B \) (again, not needed)

4. **Calculate New Moment of Inertia**:
Using the moment of inertia formula for the second bar magnet:
\[ I_2 = \frac{(2M)(2L)^2}{12} \]
Simplifying this:
\[ I_2 = \frac{(2M)(4L^2)}{12} \]
\[ I_2 = \frac{8ML^2}{12} \]
\[ I_2 = \frac{2ML^2}{3} \]

5. **Relate to the Original Moment of Inertia**:
We know from the first bar magnet that:
\[ I = \frac{ML^2}{12} \]
Thus, we can express \( I_2 \) in terms of \( I \):
\[ I_2 = 8 \left(\frac{ML^2}{12}\right) = 8I \]

6. **Final Result**:
Therefore, the moment of inertia of the second bar magnet is:
\[ I_2 = 8I \]

### Conclusion:
The moment of inertia of the second bar magnet, with all dimensions doubled, is \( 8I \).

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