A river of salty water is flowing with a velocity 2 `ms^(-1) `  If the density of the water is 1.28 c `c^(-1)`, then the kinetic momentum during a collision, the condition is energy of each cubic meter of water is

Options

A. 2.4 J
B. 24J
C. 4.8 J
D. 2.45 KJ

Answer

To solve the problem, we need to find the kinetic energy of each cubic meter of salty water flowing in the river. The steps to arrive at the solution are as follows:

### Step 1: Convert Density to Standard Units
The density of the water is given as 1.28 grams per cubic centimeter (g/cm³). We need to convert this to kilograms per cubic meter (kg/m³).

1. **Conversion Factors**:
- 1 g = 10⁻³ kg
- 1 cm³ = 10⁻⁶ m³

2. **Calculation**:
\[ \text{Density} = 1.28 \, \text{g/cm}^3 = 1.28 \times 10^{-3} \, \text{kg/cm}^3 = 1.28 \times 10^{-3} \, \text{kg} \times \frac{10^6 \, \text{cm}^3}{1 \, \text{m}^3} \]
\[ = 1.28 \times 10^{3} \, \text{kg/m}^3 = 1280 \, \text{kg/m}^3 \]

### Step 2: Calculate the Mass of Water in 1 m³
Since we are considering 1 cubic meter of water, the mass (m) is equal to the density (ρ) in kg/m³:
\[ m = 1280 \, \text{kg} \]

### Step 3: Use the Kinetic Energy Formula
The kinetic energy (KE) of a moving object is given by the formula:
\[ \text{KE} = \frac{1}{2} mv^2 \]
where:
- \( m \) = mass of the water (in kg)
- \( v \) = velocity of the water (in m/s)

### Step 4: Substitute the Values
Given that the velocity \( v \) is 2 m/s:
\[ \text{KE} = \frac{1}{2} \times 1280 \, \text{kg} \times (2 \, \text{m/s})^2 \]
\[ = \frac{1}{2} \times 1280 \times 4 \]
\[ = 640 \times 4 = 2560 \, \text{J} \]

### Step 5: Convert to Kilojoules
To convert joules to kilojoules, we divide by 1000:
\[ \text{KE} = \frac{2560 \, \text{J}}{1000} = 2.56 \, \text{kJ} \]

### Final Answer
The kinetic energy of each cubic meter of water flowing in the river is **2.56 kJ**.

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