A) \[\frac{1}{2}\,({{I}_{1}}+{{I}_{2}})\,{{({{\omega }_{1}}+{{\omega }_{2}})}^{2}}\]
B) \[\frac{1}{2}\,({{I}_{1}}+{{I}_{2}})\,({{\omega }_{1}}+{{\omega }_{2}})\]
C) \[\frac{1}{2}\frac{{{({{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}})}^{2}}}{({{I}_{1}}+{{I}_{2}})}\]
D) \[\frac{1}{16}\,({{I}_{1}}+{{I}_{2}})\,{{({{\omega }_{1}}+{{\omega }_{2}})}^{2}}\]
Correct Answer: C
Solution :
From the law of conservation of Angular momentum \[(L)={{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}=({{I}_{1}}+{{I}_{2}})\omega \] Rotational kinetic energy \[=\frac{1}{2}\frac{{{L}^{2}}}{({{I}_{1}}+{{I}_{2}})}\] \[=\frac{1}{2}\frac{{{({{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}})}^{2}}}{({{I}_{1}}+{{I}_{2}})}\]You need to login to perform this action.
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