Gce Model Questions Vol1 2017 Biology Question 18

Practice objective / multiple choice question 18 from the 2017 Gce Model Questions Vol1 Biology examination.

Gce Model Questions Vol1 2017 Biology Objective / Multiple Choice Hard Difficulty
Question 18 GCE_MODEL_QUESTIONS_VOL1 • 2017 • BIOLOGY • objective

A desert rodent is approximated as a sphere. Its body mass (in grams) equals its volume in cm³ (density ≈ 1 g cm⁻³). Metabolic heat production is \(P = 0.02\,\text{W\,g}^{-1}\times m\). Heat is lost by convection with coefficient \(h = 10\;\text{W\,m}^{-2}\text{K}^{-1}\) from the surface area \(A = 4\pi r^{2}\) (r in cm, converted to m²). The ambient temperature is 30 °C and the rodent maintains a core temperature of 38 °C. (a) Determine the maximum radius \(r_{\max}\) (in cm) for which heat production equals heat loss at steady state. (b) If a fur layer reduces the effective convection coefficient by 30 %, calculate the new permissible body mass and express the percentage change relative to the original permissible mass.

Answer Options

A. Maximum radius \(r_{\max}\) ≈ 1.0 cm (permissible mass ≈ 6.0 g). With a 30 % reduction in h, the permissible radius becomes ≈ 0.70 cm (mass ≈ 2.1 g), i.e. a ≈ 65 % decrease (the new mass is about 35 % of the original).
B. Maximum radius \(r_{\max}\) ≈ 0.9 cm (permissible mass ≈ 5.4 g). With a 30 % reduction in h, the permissible radius becomes ≈ 0.63 cm (mass ≈ 1.8 g), i.e. a ≈ 67 % decrease (the new mass is about 33 % of the original).
C. Maximum radius \(r_{\max}\) ≈ 1.5 cm (permissible mass ≈ 9.0 g). With a 30 % reduction in h, the permissible radius becomes ≈ 1.05 cm (mass ≈ 3.5 g), i.e. a ≈ 61 % decrease (the new mass is about 39 % of the original).
Correct Answer D. Maximum radius \(r_{\max}\) ≈ 1.2 cm (permissible mass ≈ 7.2 g). With a 30 % reduction in h, the permissible radius becomes ≈ 0.84 cm (mass ≈ 2.5 g), i.e. a ≈ 66 % decrease (the new mass is about 34 % of the original).
Correct Answer
D
Correct Option:
Maximum radius \(r_{\max}\) ≈ 1.2 cm (permissible mass ≈ 7.2 g). With a 30 % reduction in h, the permissible radius becomes ≈ 0.84 cm (mass ≈ 2.5 g), i.e. a ≈ 66 % decrease (the new mass is about 34 % of the original).

About This Question

This is Gce Model Questions Vol1 2017 Biology Question 18. It is one of the objective questions from the 2017 Gce Model Questions Vol1 Biology examination.

Difficulty level: Hard .

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