Discs `A` and `B` are mounted on a shaft `SS` and may be connected or disconnected by a clutch `C`. The moment of inertia of disc `A` is one half that of disc `B`. With the clutch disconnected, `A` is brought up to an angular velocity `omega_(0)` .The accelerating torque is then removed from `A` and it is coupled to disc `B` by the clutch (Bearing friction may be neglected). It is found that `2000 J` of heat is developed in the clutch when the connection is made. What is the original kinetic energy of disc `A`?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Moments of Inertia
Let the moment of inertia of disc A be \( I_A = I \) and the moment of inertia of disc B be \( I_B = 2I \) (since it is given that the moment of inertia of disc A is half that of disc B).

### Step 2: Calculate Initial Angular Momentum
When disc A is rotating with an angular velocity \( \omega_0 \), the initial angular momentum \( L_i \) of disc A is given by:
\[
...