Question

The heart of a man pumps $5 \,L$ 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 $g=10 \,ms ^{-2}$, then the power of heart in watt is

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

Answer 1

Answer: (A)

Given, pressure $=150 \,mm$ of $Hg =0.15\, m$ of $Hg$
$\rho=13.6 \times 10^{3}\, kg \,m ^{-3}, g=10 \,ms ^{-2}$
$h=0.15\, m , V=5 \times 10^{-3} \,m ^{3}$ and $t=60\, s$
Pumping rate of heart of a man $=\frac{d V}{d t}=\frac{5 \times 10^{-3}}{60} \,m ^{3} \,s ^{-1}$
Power of heart $=p \cdot \frac{d V}{d t}=\rho g h \cdot \frac{d V}{d t} \,\,\,(\because p=\rho g h)$
$=\frac{\left(13.6 \times 10^{3} \,kg\, m ^{-3}\right)(10) \times\left(0.15 \times 5 \times 10^{-3}\right)}{60}$
$=1.70 \,W$