Different units of density are kg `m^(-3)`, " g " `cm^(-3)`, " kg " `cm^(-3)` and " g " `m^(-3)`.Arrange the following steps in a sequential order to write the ascending order of these units.

Options

A. (a) a d c b
B. (b) c b d a
C. (c ) a b d c
D. (d) a d b c

Explanation

To arrange the units of density \( \text{kg m}^{-3} \), \( \text{g cm}^{-3} \), \( \text{kg cm}^{-3} \), and \( \text{g m}^{-3} \) in ascending order, we will convert all units to a common base. The most convenient base will be \( \text{kg m}^{-3} \).

### Step-by-Step Solution:

1. **Identify the Units**:
- \( A = \text{kg m}^{-3} \)
- \( B = \text{g cm}^{-3} \)
- \( C = \text{kg cm}^{-3} \)
- \( D = \text{g m}^{-3} \)

2. **Convert All Units to \( \text{kg m}^{-3} \)**:
- **For \( A \)**: It is already in \( \text{kg m}^{-3} \).
\[ A = 1 \text{ kg m}^{-3} \]

- **For \( B \)**: Convert \( \text{g cm}^{-3} \) to \( \text{kg m}^{-3} \).
\[ 1 \text{ g} = 0.001 \text{ kg} \quad \text{and} \quad 1 \text{ cm}^{3} = 10^{-6} \text{ m}^{3} \]
Therefore,
\[ B = \frac{0.001 \text{ kg}}{10^{-6} \text{ m}^{3}} = 1000 \text{ kg m}^{-3} \]

- **For \( C \)**: Convert \( \text{kg cm}^{-3} \) to \( \text{kg m}^{-3} \).
\[ C = \frac{1 \text{ kg}}{10^{-6} \text{ m}^{3}} = 10^{6} \text{ kg m}^{-3} \]

- **For \( D \)**: Convert \( \text{g m}^{-3} \) to \( \text{kg m}^{-3} \).
\[ D = \frac{0.001 \text{ kg}}{1 \text{ m}^{3}} = 0.001 \text{ kg m}^{-3} \]

3. **List the Converted Values**:
- \( A = 1 \text{ kg m}^{-3} \)
- \( D = 0.001 \text{ kg m}^{-3} \)
- \( B = 1000 \text{ kg m}^{-3} \)
- \( C = 10^{6} \text{ kg m}^{-3} \)

4. **Arrange in Ascending Order**:
- The order from smallest to largest is:
\[ D < A < B < C \]
- In terms of the original units, this corresponds to:
\[ D (\text{g m}^{-3}) < A (\text{kg m}^{-3}) < B (\text{g cm}^{-3}) < C (\text{kg cm}^{-3}) \]

### Final Answer:
The ascending order of the units of density is:
\[ \text{g m}^{-3} < \text{kg m}^{-3} < \text{g cm}^{-3} < \text{kg cm}^{-3} \]