Two coaxial discs, having moments of inertia $I _ { 1 }$ and $\frac { I _ { 1 } } { 2 }$, are rotating with respective angular velocities $\omega _ { 1 }$ and $\frac { \omega _ { 1 } } { 2 }$, 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 $\left( E _ { f } - E _ { i } \right)$ is: (1) $\frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 6 }$ (2) $\frac { 3 } { 8 } I _ { 1 } \omega _ { 1 } ^ { 2 }$ (3) $- \frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 12 }$ (4) $- \frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 24 }$
Two coaxial discs, having moments of inertia $I _ { 1 }$ and $\frac { I _ { 1 } } { 2 }$, are rotating with respective angular velocities $\omega _ { 1 }$ and $\frac { \omega _ { 1 } } { 2 }$, 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 $\left( E _ { f } - E _ { i } \right)$ is:\\
(1) $\frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 6 }$\\
(2) $\frac { 3 } { 8 } I _ { 1 } \omega _ { 1 } ^ { 2 }$\\
(3) $- \frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 12 }$\\
(4) $- \frac { I _ { 1 } \omega _ { 1 } ^ { 2 } } { 24 }$