Two co-axial rotors having moments of inertia \(I_{1}, I_{2}\) and angular speeds \(\omega_{1}\) and \(\omega_{2}\) respectively are engaged together. The loss of energy during engagment is equal to

(a) \(\frac{I_{1} I_{2}\left(\omega_{1}-\omega_{2}\right)^{2}}{2\left(I_{1}+I_{2}\right)}\)

(b) \(\frac{I_{1} I_{2}\left(\omega_{1}^{2}-\omega_{2}^{2}\right)^{2}}{2\left(I_{1}+I_{2}\right)}\)

(c) \(\frac{2 I_{1} I_{2}\left(\omega_{1}-\omega_{2}\right)^{2}}{\left(I_{1}+I_{2}\right)}\)

(d) \(\frac{I_{1} \omega_{1}^{2}+I_{2} \omega_{2}^{2}}{\left(I_{1}+I_{2}\right)}\).