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

Answer

B

Explanation

`DeltaKE =(1)/(2) (I_(1)I_(2))/(I_(1)+I_(2))(omega_(1)-omega_(2))^(2)`
` =(1)/(2) (I^(2))/((2I))(omega_(1)-omega_(2))^(2)`
` =(1)/(4) I(omega_(1)-omega_(2))^(2)`