Question

Given below are two statements:
Statement (I): The fineness modulus indicates the uniformity of grind in the resultant product of a feed grinder.
Statement (II): The uniformity index indicate distribution of fines and coarses in the resultant product.
In light of the above statements, choose the most appropriate answer from the options given below.

• A. Both Statement (I) and Statement (II) are correct.
• B. Both Statement (I) and Statement (II) are incorrect.
• C. Statement (I) is correct but Statement (II) is incorrect.
• D. Statement (I) is incorrect but Statement (II) is correct.

Hint:

Fineness modulus only indicates the average size of the particles, not how uniform the grind is.
A uniform batch and a highly varied batch can mathematically have the same fineness modulus.

Answer 1

The Correct Option is D

Step 1: Examine what fineness modulus actually measures.
Fineness modulus is calculated by summing the cumulative percentage of ground material retained on a fixed series of sieves and dividing that sum by 100. This single number moves up or down mainly with the average particle size of the product, a coarser grind gives a higher fineness modulus, it does not by itself tell you how spread out or how uniform the mixture of particle sizes is. So Statement (I), which calls fineness modulus an indicator of uniformity of grind, misrepresents what the index measures and is incorrect.
Step 2: Examine what the uniformity index measures.
The uniformity index (closely related to the geometric standard deviation of the particle size distribution) is specifically built to describe the spread of fine and coarse particles around the mean size, a value near one indicates a tightly grouped, uniform product while a larger value indicates a wide mixture of fine and coarse fragments.
Step 3: Match the statements to these definitions.
This is exactly the distinction between the two indices, fineness modulus reports the average size while the uniformity index reports the spread or distribution of fines and coarses, so Statement (II) is correct while Statement (I) is incorrect.
\[ \boxed{Statement (I) is incorrect but Statement (II) is correct.} \]