Calculate the kinetic energy of rolling ring of mass 0.2 kg about an axis passing through its centre of mass and perpendicular to it, if centre of mass is moving with a velocity of 3 m/s.

Explanation

To calculate the kinetic energy of a rolling ring, we need to consider both its translational and rotational kinetic energy. Here’s a step-by-step solution:

### Step 1: Identify the Given Values
- Mass of the ring, \( m = 0.2 \, \text{kg} \)
- Velocity of the center of mass, \( v = 3 \, \text{m/s} \)

### Step 2: Write the Formula for Total Kinetic Energy
The total kinetic energy \( K \) of a rolling object is the sum of its translational kinetic energy \( K_t \) and rotational kinetic energy \( K_r \):
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