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

Concept: Density is defined as the mass per unit volume of a substance. \[ \rho = \frac{m}{V} \] where
• \( \rho \) = density
• \( m \) = mass
• \( V \) = volume For a cube, the volume is given by \[ V = a^3 \] where \(a\) is the edge length of the cube.

Step 1: Calculate the volume of the cube. Edge of cube: \[ a = 4 \text{ cm} \] \[ V = a^3 = 4^3 = 64 \text{ cm}^3 \]

Step 2: Calculate density in CGS unit. Mass given: \[ m = 256 \text{ g} \] \[ \rho = \frac{256}{64} = 4 \text{ g/cm}^3 \]

Step 3: Convert density into SI unit. \[ 1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3 \] Therefore, \[ 4 \text{ g/cm}^3 = 4 \times 1000 \] \[ = 4000 \text{ kg/m}^3 \] Thus, the density of the material is \[ \boxed{4000 \,\text{kg/m}^3} \]