Question

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

• A. 3.0
• B. 1.50
• C. 1.70
• D. 2.35

Answer 1

Answer: (C)

Here,
Volume of blood pumped by man's heart,
$V =5$ litres $=5 \times 10^{-3} m ^{3} \left(\because 1\right.$ litre $\left.=10^{-3} m ^{3}\right)$
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 $Hg$
$=(0.15 m )\left(13.6 \times 10^{3} \,kg / m ^{3}\right)\left(10\,m / s ^{2}\right)$
$(\because P=h \rho \,g)$
$=20.4 \times 10^{3} \,N / m ^{2}$
$\therefore$ Power of the heart $=\frac{P V}{t}$
$=\frac{\left(20.4 \times 10^{3} N / m ^{2}\right)\left(5 \times 10^{-3} m ^{3}\right)}{60 s }=1.70\, W$