35. In hydrotherapy training at KMU, a therapist measures a patient's body density using underwater weighing. A patient has a mass of 75.0 kg in air. When fully submerged in water, the apparent mass is 3.0 kg. Assume water density ρ = 1.0 g/cm³ and neglect lung air volume changes. What is the patient's body density?
(A) 0.960 kg/m³
(B) 1.042 kg/m³
(C) 960 kg/m³
(D) 1042 kg/m³
(E) 1120 kg/m³

36. A hospital keeps oxygen cylinders in an emergency room. An oxygen cylinder contains gas at a gauge pressure of 220 kPa at a temperature of 27 °C. During transportation in summer, the cylinder temperature rises to 47 °C. What is the new gauge pressure inside the cylinder? Assume the cylinder volume is constant, oxygen behaves as an ideal gas, and atmospheric pressure is 100 kPa. (A) 234 kPa (B) 241 kPa (C) 331 kPa (D) 334 kPa (E) 341 kPa

37. During a liver ultrasound scan, the transducer operates at frequency f = 5.0 MHz. The sound speed in liver tissue is v = 1540 m/s. The emitted ultrasound pulse contains 3 cycles per pulse (i.e., the spatial pulse length (SPL) corresponds to 3 wavelengths). Assume the minimum separable distance along the beam direction (axial resolution) is Δzmin = SPL/2. What is the minimum tumor thickness (along the beam direction) that can be resolved as a distinct structure? (A) 0.15 mm (B) 0.23 mm (C) 0.46 mm (D) 0.92 mm (E) 1.54 mm

38. The deformation and the restoring force of an elastic string obey Hooke's law. When the string is stretched to twice its original length, the speed of transverse waves on the string is v. What is the wave speed on the string when it is stretched to four times its original length? Assume the mass of the string remains constant and is uniformly distributed. (A) v (B) (C) (D) 2v (E)

39. A supersonic jet fighter flies horizontally at a constant altitude of 3400 m with a speed of Mach 1.25. Assuming the speed of sound is 340 m/s, how much time will elapse after the jet passes directly over an observer before the shock wave (sonic boom) reaches them? (A) 4.00 s (B) 6.00 s (C) 7.50 s (D) 8.00 s (E) 10.0 s

40. An ideal monatomic gas expands from volume V₀ to 2V₀ along a straight line path in the P-V (pressure-volume) diagram from (P₀, V₀) to (P₀/2, 2V₀). What is the heat Q absorbed by the gas in this process? (A) 0.75P₀V₀ (B) P₀V₀ (C) 1.25P₀V₀ (D) 1.5P₀V₀ (E) 2P₀V₀

41. A cylindrical rod of length L and radius R is insulated on its surface. Its thermal conductivity k varies with temperature as k(T) = αT. If the two ends of the rod are maintained at T₁ and T₂, the heat current dQ/dt is proportional to ______. (A) ln(T₁/T₂) (B) (C) T₁ - T₂ (D) T₁² - T₂² (E) T₁³ - T₂³

42. The figure represents a closed cycle for an ideal gas (the figure is not drawn to scale). The change in the internal energy of the gas as it moves from a to c along the path abc is -500 J. As the gas moves from state c to state d, 400 J of heat is transferred to the system. An additional 200 J of heat is absorbed by the gas as it moves from d back to a. What is the work done on the gas as it moves from c to d? (A) -100 J (B) 100 J (C) -300 J (D) 300 J (E) -700 J

43. A heat engine operates between a high-temperature reservoir at 500 K and a low-temperature reservoir at 300 K. In each cycle, the engine absorbs 1000 J of heat from the high-temperature reservoir and performs 500 J of work. Which of the following statements regarding this engine is correct? (A) It violates the first law of thermodynamics but not the second. (B) It violates the second law of thermodynamics but not the first. (C) It violates both the first and second laws of thermodynamics. (D) It violates neither law and is theoretically possible. (E) There is insufficient information to determine if any laws are violated.

44. A gas is at 200 K. If we wish to double the root-mean-square speed of the molecules of the gas, to what value must we raise its temperature? (A) 283 K (B) 400 K (C) 566 K (D) 800 K (E) 1130 K

45. A long coaxial cable consists of a solid inner conductor of radius a carrying current I and a thin outer shell of radius b carrying return current I. The magnetic field at distance r (a ＜ r ＜ b) is ______. (Given: permeability constant μ₀) (A) 0 (B) μ₀I/(2πa) (C) μ₀I/(2πr) (D) μ₀Ir/(2πab) (E) μ₀I/(2πb)

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