Question

A river of salty water is flowing with a velocity of $2m{s}^{-1}$ If the density of the water is$1.2g/cc$ then the kinetic energy of each cubic metre of water is

• A. $2.4J$
• B. $24J$
• C. $2.4KJ$
• D. $4.8KJ$

Answer 1

The correct option is C

$2.4KJ$

Step 1. Given Data,

Velocity $V=2m{s}^{-1}$

Density of Water $\rho =1.2g/cc$

We know that Volume of Water $v=1m^3$

Let the mass of each cube be $m$ and the Kinetic Energy be $K$.

Step 2. We have to calculate the Kinetic Energy $K$,

We know that,

Mass $=$Density $/$Volume

$$\begin{gathered} \Rightarrow m=\frac{\rho }{v} \\ \Rightarrow m=\frac{1.2\times {10}^{-3}}{{\left({10}^{-2}\right)}^3} \\ \Rightarrow m=1.2\times {10}^{3}Kg \end{gathered}$$

Therefore, Kinetic Energy,

$$\begin{gathered} K=\frac{1}{2}m{v}^2 \\ \Rightarrow K=\frac{1}{2}\times \left(1.2\times 10{}^3\right)\times {\left(2\right)}^2 \\ \Rightarrow K=2.4\times {10}^{3}J \\ \Rightarrow K=2.4KJ \end{gathered}$$

Therefore, the Kinetic Energy $K=2.4KJ$.

Hence, the correct option is $\text{'}C\text{'}$