Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

1.7

2.35

1.5

Step-by-Step Solution

Identify the Formula: The power ( $P_{ower}$ ) delivered by a pump (like the heart) moving a fluid is given by the product of the pressure ( $P$ ) and the volume flow rate ( $\frac{dV}{dt}$ ). $P_{ower} = P \times \frac{dV}{dt}$ (Derived from $P_{ower} = \vec{F} \cdot \vec{v} = (P \cdot A) \cdot v = P \cdot (Av) = P \cdot \frac{dV}{dt}$ )
Convert Units to SI:

Volume flow rate: $\frac{dV}{dt} = 5 \text{ L/min} = \frac{5 \times 10^{-3} \text{ m}^3}{60 \text{ s}} = \frac{5}{6} \times 10^{-4} \text{ m}^3/\text{s}$ .
Pressure head ( $h$ ): $150 \text{ mm} = 0.15 \text{ m}$ .
Density ( $\rho$ ): $13.6 \times 10^3 \text{ kg/m}^3$ .
Gravity ( $g$ ): $10 \text{ m/s}^2$ .

Calculate Pressure ( $P$ ): Using the hydrostatic pressure formula: $P = h\rho g = 0.15 \times (13.6 \times 10^3) \times 10$ $P = 20400 \text{ N/m}^2 \text{ (Pa)}$
Calculate Power: $P_{ower} = 20400 \times \left( \frac{5 \times 10^{-3}}{60} \right)$ $P_{ower} = \frac{20400 \times 5}{60000} = \frac{102}{60} = 1.70 \text{ W}$

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