A river of salty water is flowing with a velocity $2 \mathrm{~m} / \mathrm{s}$. If the density of the water…
A river of salty water is flowing with a velocity $2 \mathrm{~m} / \mathrm{s}$. If the density of the water is $1.2 \mathrm{~g} / \mathrm{cc}$, then the kinetic energy of each cubic metre of water is
$2.4 \mathrm{~J}$
$24 \mathrm{~J}$
$2.4 \mathrm{~kJ}$
$4.8 \mathrm{~kJ}$
Solution
Given, velocity of river, $(v)=2 \mathrm{~m} / \mathrm{s}$
Density of water
$\rho=1.2 \mathrm{~g} / \mathrm{cc}$
Mass of each cubic metre
$
m=\frac{1.2 \times 10^{-3}}{\left(10^{-2}\right)^3}=1.2 \times 10^3 \mathrm{~kg}
$
$
\begin{aligned}
\therefore \quad \text { Kinetic energy } & =\frac{1}{2} m v^2 \\
& =\frac{1}{2} \times 1.2 \times 10^3 \times(2)^2 \\
& =2.4 \times 10^3 \mathrm{~J}=2.4 \mathrm{~kJ}
\end{aligned}
$