A body of mass` 5 kg` is moving with a momentum of `10 kg m//s`. A force of `0.2 N` acts on it in the direction of motion of the body for `10 sec.` The increase in its kinetic energy.

Options

A. `2.8 J`
B. `3.2 J`
C. `3.8 J`
D. `4.4 J`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Initial Kinetic Energy
The formula for kinetic energy (KE) in terms of momentum (p) is given by:

\[ KE = \frac{p^2}{2m} \]

Given:
- Momentum \( p = 10 \, \text{kg m/s} \)
- Mass \( m = 5 \, \text{kg} \)

Substituting the values:

\[ KE_{\text{initial}} = \frac{10^2}{2 \times 5} = \frac{100}{10} = 10 \, \text{J} \]

### Step 2: Calculate the Impulse
Impulse (J) is the product of force (F) and the time (t) for which the force acts:

\[ J = F \times t \]

Given:
- Force \( F = 0.2 \, \text{N} \)
- Time \( t = 10 \, \text{s} \)

Substituting the values:

\[ J = 0.2 \times 10 = 2 \, \text{N s} \]

### Step 3: Calculate the Change in Momentum
Impulse is also equal to the change in momentum (\( \Delta p \)):

\[ \Delta p = J \]

Thus, the change in momentum is:

\[ \Delta p = 2 \, \text{kg m/s} \]

### Step 4: Calculate the Final Momentum
The final momentum (\( p_f \)) can be calculated as:

\[ p_f = p_i + \Delta p \]

Where \( p_i \) is the initial momentum:

\[ p_f = 10 + 2 = 12 \, \text{kg m/s} \]

### Step 5: Calculate the Final Kinetic Energy
Using the final momentum to find the final kinetic energy:

\[ KE_{\text{final}} = \frac{p_f^2}{2m} \]

Substituting the values:

\[ KE_{\text{final}} = \frac{12^2}{2 \times 5} = \frac{144}{10} = 14.4 \, \text{J} \]

### Step 6: Calculate the Increase in Kinetic Energy
The increase in kinetic energy (\( \Delta KE \)) is given by:

\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \]

Substituting the values:

\[ \Delta KE = 14.4 - 10 = 4.4 \, \text{J} \]

### Final Answer
The increase in kinetic energy is \( 4.4 \, \text{J} \).

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