Two coaxial discs, having moments of inertia I 1 and I 1 2 , are rotating with respective angular velocities ω 1 and ω 1 2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E f and E i are the final and initial total energies, then E f - E i is:

Step-by-step solution

As external torque is zero, angular momentum remains conserved. I 1 ω 1 + I 1 2 ω 1 2 = I 1 + I 1 2 ω ∴ Common angular velocity ω = 5 ω 1 6 ∴ E f - E i = 1 2 × I 1 + I 1 2 ω 2 - 1 2 × I 1 ω 1   2 - 1 2 × I l 2 ω 1 2 2 = 1 2 × 3 I 1 2 5 6 ω 1 2 - 9 16 I 1 ω 1 2 = 75   I 1 ω 1 2 - 81   I 1 ω 1 2 144 = - 6 I 1 ω 1 2 144 = - I 1 ω 1 2 24