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)/(9) I(omega_1 - omega_2)^2`
D. `(1)/(2) I(omega_1 + omega_2)^2`

Answer

A

Explanation

(a) COAM, `I omega_1 = I omega_2 = 2 I omega rArr omega = (omega_1 + omega_2)/(2)`
`(K.E.)_i = (1)/(2) I omega_1^2 + (1)/(2) I omega_2^2`
`(K.E.)_f = (1)/(2) xx 2 I omega^2 = I((omega_1 + omega_2)/(2))^2`
Loss in `K.E. =(K.E)_i - (K.E.)_f = (1)/(4) (omega_1 - omega_2)^2`.