question_answer

\[{{I}_{1}}\] and \[{{I}_{2}}\] are the moments of inertia of two circular discs about their central axes perpendicular to their surfaces. Their angular frequencies of rotation are \[{{\omega }_{1}}\] and \[{{\omega }_{2}}\] respectively. If they are brought into contact face to face with their axes of rotation coinciding with each other, the angular frequency of the composite disc will be

A)  \[\frac{{{I}_{1}}+{{I}_{2}}}{{{\omega }_{1}}+{{\omega }_{2}}}\]

B)  \[\frac{{{I}_{2}}{{\omega }_{1}}-{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}-{{I}_{2}}}\]

C)  \[\frac{{{I}_{2}}{{\omega }_{1}}+{{I}_{1}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]

D)  \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\]