A mass of `5kg` is moving along a circular path or radius `1m`. If the mass moves with 300 revolutions per minute, its kinetic energy would be

Options

A. `250pi^2 J`
B. `100 pi^2 J`
C. `5pi^2 J`
D. 0 J

Explanation

To solve the problem, we need to find the kinetic energy of a mass moving in a circular path. Here’s the step-by-step solution:

### Step 1: Write down the given data
- Mass (m) = 5 kg
- Radius (r) = 1 m
- Revolutions per minute (RPM) = 300

### Step 2: Calculate the distance covered in one revolution
The distance covered in one revolution (circumference of the circle) is given by the formula:
\[ \text{Distance in one revolution} = 2 \pi r \]
Substituting the value of r:
\[ \text{Distance in one revolution} = 2 \pi \times 1 = 2\pi \text{ meters} \]

### Step 3: Calculate the total distance covered in 300 revolutions
The total distance covered in 300 revolutions is:
\[ \text{Total distance} = 300 \times 2\pi = 600\pi \text{ meters} \]

### Step 4: Calculate the total time taken
Since the mass makes 300 revolutions in 1 minute, we convert this to seconds:
\[ \text{Total time} = 60 \text{ seconds} \]

### Step 5: Calculate the velocity (v)
Velocity is defined as the total distance covered divided by the total time taken:
\[ v = \frac{\text{Total distance}}{\text{Total time}} = \frac{600\pi}{60} = 10\pi \text{ meters/second} \]

### Step 6: Calculate the kinetic energy (KE)
The kinetic energy is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
Substituting the values of m and v:
\[ KE = \frac{1}{2} \times 5 \times (10\pi)^2 \]
Calculating \( (10\pi)^2 \):
\[ (10\pi)^2 = 100\pi^2 \]
Now substituting this back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 5 \times 100\pi^2 = \frac{500\pi^2}{2} = 250\pi^2 \text{ Joules} \]

### Final Answer
The kinetic energy of the mass is:
\[ KE = 250\pi^2 \text{ Joules} \]

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