A milk fat globule of 2 µm diameter is rising in whole milk of density 1030 kg m⁻³ and coefficient of viscosity 10⁻³ Poise [as reproduced from the scan]. If the fat density is 950 kg m⁻³, the time needed to rise 10 mm for this fat globule in min is
Options:
(A) 0.57
(B) 34.57
(C) 35.57
(D) 95.57
Official Answer Key:
D
Step-by-Step Solution & Explanation
Stokes' law (creaming/rise velocity under gravity): v = d²(ρ_milk−ρ_fat)g/(18μ).
Using μ = 10⁻³ Poise = 10⁻⁴ Pa·s (as literally transcribed):
v = (2×10⁻⁶)²×(1030−950)×9.81/(18×10⁻⁴) = 4×10⁻¹²×80×9.81/0.0018 = 1.744×10⁻⁶ m/s.
Time to rise 10 mm = 0.01/1.744×10⁻⁶ = 5734 s = 95.6 min, matching option (D). *(If milk's actual viscosity, ~1.5×10⁻² Poise, were used instead, the rise time would be roughly 15–20× longer than any of the listed options — supporting that the intended viscosity value is as transcribed above, or that a different diameter/depth was intended in the original.)*
Appendix A — Consolidated Answer Table
No official key was available; the "Answer" column below is our independently derived value for each question.
Appendix B — Section-wise Weightage
Preparation observations
• This 2013 paper's weightage pattern differs somewhat from GATE 2023: Farm Power, Farm Machinery, Soil & Water Conservation Engineering, and Irrigation & Drainage Engineering are all substantial and roughly balanced (8 questions each), rather than one section dominating.
• The 2013 paper features two Common Data pairs and two Linked Answer pairs — a format later phased out of GATE. These multi-part problems reward careful unit-tracking and staged calculation, since an error in the first question of a linked pair propagates to the second.
• Several questions in this paper (Q.3, Q.11, Q.19, Q.26, Q.47) had partially garbled source text — equations, option lettering, or a numeric value did not scan cleanly. Each is flagged with a transcription note explaining the interpretation used; treat these specific answers with more caution than the rest.
• No official answer key was available for this paper. Every answer in this document is independently derived using standard formulas and first-principles reasoning — none were cross-checked against an official source. Independent verification is strongly recommended before relying on these for exam preparation.
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