A body of mass 5kg at rest is acted upon by two mutually perpendicular forces 6N and 8N simultaneously. Its kinetic energy after 10s is

Options

A. 100J
B. 200J
C. 500J
D. 1000J

Answer

To solve the problem step by step, we will follow the outlined approach in the video transcript.

### Step 1: Identify the Forces
We have two forces acting on the body:
- Force 1 (F1) = 6 N
- Force 2 (F2) = 8 N

These forces are acting perpendicularly to each other.

### Step 2: Calculate the Resultant Force
To find the net force acting on the body, we can use the Pythagorean theorem since the forces are perpendicular.

\[ F_{\text{net}} = \sqrt{F_1^2 + F_2^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{N} \]

### Step 3: Calculate the Acceleration
Using Newton's second law of motion, we can find the acceleration (a) of the body.

\[ a = \frac{F_{\text{net}}}{m} \]

Where:
- \( F_{\text{net}} = 10 \, \text{N} \)
- \( m = 5 \, \text{kg} \)

Substituting the values:

\[ a = \frac{10 \, \text{N}}{5 \, \text{kg}} = 2 \, \text{m/s}^2 \]

### Step 4: Calculate the Final Velocity
Since the body is initially at rest, we can use the first equation of motion to find the final velocity (v) after 10 seconds.

\[ v = u + at \]

Where:
- \( u = 0 \, \text{m/s} \) (initial velocity)
- \( a = 2 \, \text{m/s}^2 \)
- \( t = 10 \, \text{s} \)

Substituting the values:

\[ v = 0 + (2 \, \text{m/s}^2 \times 10 \, \text{s}) = 20 \, \text{m/s} \]

### Step 5: Calculate the Kinetic Energy
Now we can calculate the kinetic energy (KE) of the body using the formula:

\[ KE = \frac{1}{2} mv^2 \]

Substituting the values:

\[ KE = \frac{1}{2} \times 5 \, \text{kg} \times (20 \, \text{m/s})^2 \]

Calculating \( (20 \, \text{m/s})^2 \):

\[ (20 \, \text{m/s})^2 = 400 \, \text{m}^2/\text{s}^2 \]

Now substituting this back into the kinetic energy equation:

\[ KE = \frac{1}{2} \times 5 \times 400 = \frac{2000}{2} = 1000 \, \text{J} \]

### Final Answer
The kinetic energy of the body after 10 seconds is **1000 Joules**.

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