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NEET PHYSICSMechanical Properties of FluidMedium

Question

The heart of a man pumps 5 L5 \text{ L} of blood through the arteries per minute at a pressure of 150 mm150 \text{ mm} of mercury. If the density of mercury is 13.6×103 kg/m313.6 \times 10^3 \text{ kg/m}^3 and g=10 m/s2g = 10 \text{ m/s}^2, then the power of heart in watt is:

A

1.7

B

2.35

C

3

D

1.5

Step-by-Step Solution

  1. Identify the Formula: The power (PowerP_{ower}) delivered by a pump (like the heart) moving a fluid is given by the product of the pressure (PP) and the volume flow rate (dVdt\frac{dV}{dt}). Power=P×dVdtP_{ower} = P \times \frac{dV}{dt} (Derived from Power=Fv=(PA)v=P(Av)=PdVdtP_{ower} = \vec{F} \cdot \vec{v} = (P \cdot A) \cdot v = P \cdot (Av) = P \cdot \frac{dV}{dt})
  2. Convert Units to SI:
  • Volume flow rate: dVdt=5 L/min=5×103 m360 s=56×104 m3/s\frac{dV}{dt} = 5 \text{ L/min} = \frac{5 \times 10^{-3} \text{ m}^3}{60 \text{ s}} = \frac{5}{6} \times 10^{-4} \text{ m}^3/\text{s}.
  • Pressure head (hh): 150 mm=0.15 m150 \text{ mm} = 0.15 \text{ m}.
  • Density (ρ\rho): 13.6×103 kg/m313.6 \times 10^3 \text{ kg/m}^3.
  • Gravity (gg): 10 m/s210 \text{ m/s}^2.
  1. Calculate Pressure (PP): Using the hydrostatic pressure formula: P=hρg=0.15×(13.6×103)×10P = h\rho g = 0.15 \times (13.6 \times 10^3) \times 10 P=20400 N/m2 (Pa)P = 20400 \text{ N/m}^2 \text{ (Pa)}

  2. Calculate Power: Power=20400×(5×10360)P_{ower} = 20400 \times \left( \frac{5 \times 10^{-3}}{60} \right) Power=20400×560000=10260=1.70 WP_{ower} = \frac{20400 \times 5}{60000} = \frac{102}{60} = 1.70 \text{ W}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Mechanical Properties of Fluid. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMechanical Properties of Fluidthrougharteriesminutepressuremercury

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