If a bar magnet of pole strength `'m'` and magnetic moment `'M'` is cut equally `5` times parallel to its axis and `4` times perpendicular to its axis then the pole strength and magnetic moment of each piece are respectively

Options

A. `m/20,M/20`
B. `m/4,M/20`
C. `m/5,M/20`
D. `m/5,M/4`

Answer

To solve the problem, we need to analyze how cutting the bar magnet affects its pole strength and magnetic moment.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- Let the initial pole strength of the bar magnet be \( m \).
- Let the initial magnetic moment of the bar magnet be \( M \).
- Let the length of the bar magnet be \( L \).

2. **Cutting the Magnet Parallel to the Axis**:
- The magnet is cut 5 times parallel to its axis. This means the magnet is divided into 5 equal parts along its length.
- When a magnet is cut parallel to its axis, the pole strength of each piece changes. The new pole strength \( m' \) for each piece is given by:
\[ m' = \frac{m}{5} \]

3. **Cutting the Magnet Perpendicular to the Axis**:
- Next, the magnet is cut 4 times perpendicular to its axis. This means each of the 5 pieces is further divided into 4 equal parts.
- Cutting perpendicular to the axis does not change the pole strength. Therefore, the pole strength remains:
\[ m' = \frac{m}{5} \]

4. **Calculating the New Length**:
- After cutting the magnet 4 times perpendicular to the axis, the length of each piece becomes:
\[ L' = \frac{L}{4} \]

5. **Calculating the New Magnetic Moment**:
- The magnetic moment \( M' \) of each piece is given by the formula:
\[ M' = m' \times L' \]
- Substituting the values we found:
\[ M' = \left(\frac{m}{5}\right) \times \left(\frac{L}{4}\right) = \frac{mL}{20} \]
- Since the initial magnetic moment \( M = m \times L \), we can express \( M' \) in terms of \( M \):
\[ M' = \frac{M}{20} \]

6. **Final Results**:
- The pole strength of each piece is \( \frac{m}{5} \).
- The magnetic moment of each piece is \( \frac{M}{20} \).

### Summary:
- The pole strength of each piece is \( \frac{m}{5} \).
- The magnetic moment of each piece is \( \frac{M}{20} \).