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

Let `I_(A)` and `I_(B)=2I`
In the connection of disk `A` with disk `B`, the agular momentum remains constant
or `Iomega_(0)+0=(I+2I)omega`
which gives `omega=omega_(0)//3`
The change in `KE` eveloved as eat, i.e.,
`1/2Iomega_(0)^(2)-1/2(3I)omega^(2)=2000`
Substituting the value of `omega` in the above equation, we get
`1/2Iomega_(0)^(2)-1/2(3I)((omega_(0))/3)^(2)=2000`
or `1/2 Iomega_(0)^(2)=-1/2 (Iomega_(0)^(2))/3 2000`
`:. 1/2Iomega^(2)=3000J`
Where `Iomega^(2)//2` is the initial energy of the disk `A`.