Two discs have moments of intertia `I _(1) and I _(2)` about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, `W_(1) and W_(2)` respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

Options

A. `(( I _(1) - I _(2)) ^(2) omega _(1) omega _(2))/(2I _(1) + I _(2))`
B. `( I _(1) I _(2))/(( I _(1) + I _(2)))( omega _(1) - omega _(2) ) ^(2)`
C. `( I _(1) I _(2))/( 2 ( I _(1) + I _(2))) ( omega _(1) - omega _(2)) ^(2)`
D. `(( omega _(1) - omega _(2)) ^(2))/( 2 ( I _(1) + I _(2)))`