GATE 2025 ES – Question 60
A dispersoid has spherical equal-density particles. Diameters1,10,100 µm have respective counts1000,500,10 and number-removal efficiencies99%,75%,10%. Find overall mass-removal efficiency in percent, to one decimal.
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Correct answer: 12.5 to 13.5
Explanation
Equal-density spherical particle mass is proportional to $d^3$. Weight removal by each size class’s total mass: $$\eta_m=100\frac{1000(1^3)(.99)+500(10^3)(.75)+10(100^3)(.10)}{1000(1^3)+500(10^3)+10(100^3)}=13.10342\%.$$ Answer **13.1%**. The few largest particles dominate mass despite contributing little to total number.