Question

The weight of wheat grain having moisture content 15% (dry basis) stored in a container with internal dimensions of 20x30x10 cm is 6 kg; then the bulk density of the wheat is -

• A. \(2 \text{ g/cm}^3\)
• B. \(0.5 \text{ g/cm}^3\)
• C. \(10 \text{ g/cm}^3\)
• D. \(1 \text{ g/cm}^3\)

Hint:

Always ensure your units are consistent. If mass is given in kilograms and dimensions in centimeters, converting the mass to grams makes it easy to calculate density directly in the standard metric unit of \(\text{g/cm}^3\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Bulk density (\(\rho_b\)) is defined as the mass of many particles of a material divided by the total volume they occupy. This total volume includes the volume of the particles themselves, the open pore space between the particles, and any internal pore volume within the particles.
Key Formula or Approach:
The bulk density is calculated as: \[ \rho_b = \frac{\text{Mass of material } (M)}{\text{Total volume occupied } (V)} \]

Step 2: Detailed Explanation:
Let us identify and convert the given parameters into consistent units:

Mass of stored wheat, \(M = 6 \text{ kg} = 6000 \text{ g}\)

Internal dimensions of the storage container = \(20 \text{ cm} \times 30 \text{ cm} \times 10 \text{ cm}\)

Volume of the container, \(V = 20 \times 30 \times 10 = 6000 \text{ cm}^3\)
Now, substitute these values into the bulk density formula: \[ \rho_b = \frac{6000 \text{ g}}{6000 \text{ cm}^3} = 1 \text{ g/cm}^3 \] Note: The moisture content of 15% (dry basis) is extra information. Bulk density is calculated using the total bulk mass (which already includes the moisture) divided by the total bulk volume. Thus, the moisture content does not alter this straightforward calculation.

Step 3: Final Answer:
The bulk density of the wheat is \(1 \text{ g/cm}^3\), which corresponds to Option (D).