GATE 2024 AG – Question 64
Sorghum-flour sieve analysis gives IS sieve numbers100,70,50,40,30,20,PAN with retained masses0,10.1,16.5,36.2,82.8,95.0,9.4 g. Find empirical mean particle size in mm, to three decimals.
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Correct answer: 0.230 to 0.260
Explanation
Total mass is 250 g. Cumulative retained masses on the six sieves, excluding pan, are0,10.1,26.6,62.8,145.6,240.6 g. Fineness modulus is the sum of cumulative retained percentages divided by 100,equivalently $FM=(0+10.1+26.6+62.8+145.6+240.6)/250=1.9428$. Using the customary IS-sieve empirical correlation,$D_p=.135(1.366)^{FM}=.24744996$ mm. Thus **.247 mm**. This is an empirical fineness-modulus estimate, not an arithmetic average of sieve labels.