Question

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

• A. \(4 \,\text{kg/m}^3 \)
• B. \(1600 \,\text{kg/m}^3 \)
• C. \(4000 \,\text{kg/m}^3 \)
• D. \(1000 \,\text{kg/m}^3 \)

Hint:

Remember the important conversion: \[ 1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3 \] Always convert CGS units to SI units carefully when density is asked in \(\text{kg/m}^3\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question requires calculating the density of a cube in SI units (\(\text{kg/m}^3\)) given its edge length in cm and mass in grams.
Step 2: Key Formula or Approach:
Density (\(\rho\)) is mass divided by volume:
\[ \rho = \frac{m}{V} \]
For a cube, volume \(V = \text{side}^3\).
Step 3: Detailed Explanation:
1. Find Volume in CGS:
Side \(a = 4 \text{ cm}\).
\[ V = 4^3 = 64 \text{ cm}^3 \]
2. Calculate Density in CGS:
Mass \(m = 256 \text{ g}\).
\[ \rho = \frac{256 \text{ g}}{64 \text{ cm}^3} = 4 \text{ g/cm}^3 \]
3. Convert to SI Units:
We know that \(1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3\).
\[ \rho = 4 \times 1000 \text{ kg/m}^3 = 4000 \text{ kg/m}^3 \]
Step 4: Final Answer:
The density of the material in SI units is \(4000 \text{ kg/m}^3\).