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)`
B. `100pi^(2)`
C. `5pi^(2)`
D. 0

Explanation

To find the kinetic energy of a mass moving in a circular path, we can follow these steps:

### Step 1: Understand the given values
- 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:
\[ \text{Distance} = 2 \pi r \]
Substituting the radius:
\[ \text{Distance} = 2 \pi (1) = 2 \pi \text{ meters} \]

### Step 3: Calculate the total distance covered in 300 revolutions
To find the total distance covered in 300 revolutions:
\[ \text{Total Distance} = \text{Number of Revolutions} \times \text{Distance per Revolution} \]
\[ \text{Total Distance} = 300 \times 2 \pi = 600 \pi \text{ meters} \]

### Step 4: Calculate the total time taken for 300 revolutions
Since the mass completes 300 revolutions in 1 minute (60 seconds):
\[ \text{Total Time} = 60 \text{ seconds} \]

### Step 5: Calculate the speed of the mass
Speed (v) is given by the formula:
\[ v = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values:
\[ v = \frac{600 \pi}{60} = 10 \pi \text{ meters/second} \]

### Step 6: Calculate the kinetic energy
The kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the mass and speed:
\[ KE = \frac{1}{2} (5) (10 \pi)^2 \]
Calculating \( (10 \pi)^2 \):
\[ (10 \pi)^2 = 100 \pi^2 \]
Now substituting 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:
\[ \boxed{250 \pi^2 \text{ joules}} \]