A: If a bar magnet is cut into two equal halves then magnetic dipole moment of each part is half that of the original magnet.
R: magnetic dipole moment is the product of pole strength and magnetic length.

Options

A. If both Assertion & Reason are the true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reson is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the assertion and reason question, we need to analyze both statements provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if a bar magnet is cut into two equal halves, then the magnetic dipole moment of each part is half that of the original magnet.

2. **Magnetic Dipole Moment Definition**:
- The magnetic dipole moment (μ) of a bar magnet is given by the formula:
\[ μ = m \cdot 2l \]
where \(m\) is the pole strength and \(2l\) is the length of the magnet.

3. **Cutting the Magnet**:
- When the bar magnet is cut into two equal halves, we need to consider two scenarios:
- **Transverse Cut**: If the magnet is cut perpendicular to its length, the length of each half becomes \(l\) (half of the original length \(2l\)). The pole strength remains the same.
\[ μ' = m \cdot 2l' = m \cdot 2\left(\frac{l}{2}\right) = m \cdot l \]
Thus, the new magnetic dipole moment \(μ'\) is half of the original \(μ\).

- **Longitudinal Cut**: If the magnet is cut parallel to its length, the length remains \(2l\) but the pole strength \(m'\) becomes half of the original pole strength \(m\).
\[ μ' = m' \cdot 2l = \left(\frac{m}{2}\right) \cdot 2l = m \cdot l \]
Again, the new magnetic dipole moment \(μ'\) is half of the original \(μ\).

4. **Conclusion for Assertion**:
- In both cases (transverse and longitudinal cuts), the magnetic dipole moment of each part is indeed half that of the original magnet. Therefore, the assertion is **true**.

5. **Understanding the Reason**:
- The reason states that the magnetic dipole moment is the product of pole strength and magnetic length. This is a correct statement as per the definition of magnetic dipole moment.

6. **Conclusion for Reason**:
- Since the reason correctly explains the assertion, it is also **true**.

7. **Final Conclusion**:
- Both the assertion and the reason are true, and the reason is the explanation for the assertion. Therefore, the correct answer is that both statements are true and the reason explains the assertion.