The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be and , then the power (in watt) is [2015]

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Solution

Q.
The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be $13.6 \times 10^{3} {kg/m}^{3}$ and $g = 10 {m/s}^{2}$ , then the power (in watt) is [2015]

1 3.0

2 1.50

3 1.70

4 2.35

Ans.
(3)

Here, Volume of blood pumped by man's heart,

$V = 5 litres = 5 \times 10^{- 3} m^{3} (∵ 1 litre = 10^{- 3} m^{3})$

Time in which this volume of blood pumps,

$t = 1 min = 60 s$

Pressure at which the blood pumps,

$P = 150 mm of Hg = 0.15 m of Hg$

$= (0.15 m) (13.6 \times 10^{3} {kg/m}^{3}) (10 {m/s}^{2})$

$= 20.4 \times 10^{3} {N/m}^{2}$

$∴$ Power of the heart $= \frac{P V}{t}$

$= \frac{(20.4 \times 10^{3} {N/m}^{2}) (5 \times 10^{- 3} m^{3})}{60 s} = 1.70 W$

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