Two discs of same moment of inertia rotating their regular axis passing through centre and perpendicular to the plane of disc with angular velocities `omega_(1)` and `omega_(2)`. They are brought into contact face to the face coinciding the axis of rotation. The expression for loss of enregy during this process is :

Options

A. `(1)/(4) I (omega_(1) - omega_(2))^(2)`
B. `I (omega_(1) - omega_(2))^(2)`
C. `(1)/(8)(omega_(1) - omega_(2))^(2)`
D. `(1)/(2) I (omega_(1) + omega_(2))^(2)`

Explanation

To solve the problem, we need to determine the loss of energy when two discs with the same moment of inertia are brought into contact while rotating at different angular velocities. Here’s a step-by-step solution:

### Step 1: Understand the Initial Kinetic Energy
The initial kinetic energy (KE) of each disc can be expressed using the formula:
\[ KE = \frac{1}{2} I \omega^2 \]
where \(I\) is the moment of inertia and \(\omega\) is the angular velocity.
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