The kinetic energy of a body of mass 4 kg and momentum 6 N-s will be

Options

A. 4.5 J
B. 2.5 J
C. 5.5 J
D. 3.5 J

Explanation

To find the kinetic energy of a body with a given mass and momentum, we can use the relationship between kinetic energy (KE), momentum (P), and mass (m). Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass (m) = 4 kg
- Momentum (P) = 6 N·s

### Step 2: Recall the formula for kinetic energy
The kinetic energy (KE) of an object can be expressed in terms of its mass and velocity:
\[ KE = \frac{1}{2} m v^2 \]

### Step 3: Relate momentum to mass and velocity
Momentum (P) is defined as:
\[ P = m \cdot v \]
From this, we can express velocity (v) in terms of momentum and mass:
\[ v = \frac{P}{m} \]

### Step 4: Substitute velocity into the kinetic energy formula
Now, we can substitute the expression for velocity into the kinetic energy formula:
\[ KE = \frac{1}{2} m \left(\frac{P}{m}\right)^2 \]

### Step 5: Simplify the equation
Substituting \( v = \frac{P}{m} \) into the kinetic energy formula gives:
\[ KE = \frac{1}{2} m \cdot \frac{P^2}{m^2} \]
This simplifies to:
\[ KE = \frac{P^2}{2m} \]

### Step 6: Substitute the known values into the equation
Now we can substitute the known values of momentum and mass into the equation:
\[ KE = \frac{(6 \, \text{N·s})^2}{2 \cdot (4 \, \text{kg})} \]

### Step 7: Calculate the kinetic energy
Calculating the numerator:
\[ (6 \, \text{N·s})^2 = 36 \, \text{N}^2\text{s}^2 \]
Now substituting this into the equation:
\[ KE = \frac{36 \, \text{N}^2\text{s}^2}{8 \, \text{kg}} = \frac{36}{8} \, \text{J} = 4.5 \, \text{J} \]

### Final Answer
The kinetic energy of the body is:
\[ \text{KE} = 4.5 \, \text{J} \]

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