Question

A cube of edge 4 cm has mass 256 g. The density of the material in SI unit is:

• A. 4 kg/m$^3$
• B. 1600 kg/m$^3$
• C. 4000 kg/m$^3$
• D. 1000 kg/m$^3$

Hint:

Always be careful with units. You can convert to SI units at the very beginning (mass = 0.256 kg, edge = 0.04 m) or at the end. Often converting at the end is easier to avoid working with many leading zeros.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to calculate the density of a cubic material and convert the final value into the SI unit (kg/m$^3$).
Step 2: Key Formula or Approach:
1. Volume of a cube (\( V \)) = \( (\text{edge})^3 \).
2. Density (\( \rho \)) = \( \text{Mass} / \text{Volume} \).
3. Conversion: To convert from g/cm$^3$ to kg/m$^3$, multiply the value by 1000.
Step 3: Detailed Explanation:
1. Calculate Volume:
The edge length is given as 4 cm.
\[ V = 4 \text{ cm} \times 4 \text{ cm} \times 4 \text{ cm} = 64 \text{ cm}^3 \]
2. Calculate Density in CGS units:
Mass is given as 256 g.
\[ \rho = \frac{256 \text{ g}}{64 \text{ cm}^3} = 4 \text{ g/cm}^3 \]
3. Convert to SI unit:
Since \( 1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3 \):
\[ \rho = 4 \times 1000 = 4000 \text{ kg/m}^3 \]
Step 4: Final Answer:
The density of the cube in SI units is 4000 kg/m$^3$.