A body of mass 2 kg is projected vertically up with a velocity of `100 ms^(-1)`. If it rises to a height of 400 m, the energy utilized to overcome friction is (g = `10 ms^(-2)`)

Options

A. 10 KJ
B. 8 Kj
C. 1 Kj
D. 2 Kj

Answer

To solve the problem step by step, we will calculate the initial kinetic energy of the body, the potential energy at the maximum height it reaches, and then find the energy utilized to overcome friction.

### Step 1: Calculate the Kinetic Energy (KE)
The formula for kinetic energy is given by:

\[ KE = \frac{1}{2} m v^2 \]

Where:
- \( m \) = mass of the body = 2 kg
- \( v \) = initial velocity = 100 m/s

Substituting the values:

\[ KE = \frac{1}{2} \times 2 \, \text{kg} \times (100 \, \text{m/s})^2 \]

Calculating \( (100 \, \text{m/s})^2 \):

\[ (100 \, \text{m/s})^2 = 10000 \, \text{m}^2/\text{s}^2 \]

Now substituting this back into the kinetic energy formula:

\[ KE = \frac{1}{2} \times 2 \times 10000 = 10000 \, \text{J} \]

### Step 2: Calculate the Potential Energy (PE) at Maximum Height
The formula for potential energy is given by:

\[ PE = mgh \]

Where:
- \( m \) = mass of the body = 2 kg
- \( g \) = acceleration due to gravity = 10 m/s²
- \( h \) = height = 400 m

Substituting the values:

\[ PE = 2 \, \text{kg} \times 10 \, \text{m/s}^2 \times 400 \, \text{m} \]

Calculating:

\[ PE = 2 \times 10 \times 400 = 8000 \, \text{J} \]

### Step 3: Calculate the Energy Utilized to Overcome Friction
The energy utilized to overcome friction can be found by subtracting the potential energy from the kinetic energy:

\[ \text{Energy utilized to overcome friction} = KE - PE \]

Substituting the values we calculated:

\[ \text{Energy utilized to overcome friction} = 10000 \, \text{J} - 8000 \, \text{J} = 2000 \, \text{J} \]

### Final Answer
The energy utilized to overcome friction is **2000 Joules**.

---