Work Energy and Power - Result Question 35
38. The heart of 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 of heart in watt is :
(a) 2.35
(b) 3.0
(c) 1.50
(d) 1.70
[2015 RS]
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Answer:
Correct Answer: 38. (d)
Solution:
- (d) Work done by the heart, $W=P \Delta V$
where, pressure $P=\rho g h$
and $h=150 mm-0.15 m$
$ \begin{aligned} & g=10 m / sec^{2} \\ & \rho=13.6 \times 10^{3} kg / m^{3} \end{aligned} $
So, Power $=\frac{W}{t}=\frac{P \cdot \Delta V}{t}$
Power $=\frac{\rho g h \times 5 \times 10^{-3}}{60}$
$\Rightarrow \frac{13.6 \times 10^{3} \times 10 \times 0.15 \times 5 \times 10^{-3}}{60}$
$\Rightarrow 1.7$ watt
Power $\vec{F} \cdot \vec{V}=P A \vec{V}=\rho g h A V$
$[\because P=\frac{F}{A}.$ and $.P=\rho g h]$
$\therefore P=13.6 \times 10^{3} \times 10 \times 150 \times 10^{-3} \times 0.5 \times 10^{-3} / 60$
$=\frac{102}{60}=1.70$ watt
