A) \[\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{2({{I}_{1}}+{{I}_{2}})}\]
B) \[\frac{({{I}_{1}}+{{I}_{2}})\,{{({{\omega }_{1}}+{{\omega }_{2}})}^{2}}}{2}\]
C) \[\frac{({{I}_{1}}\omega {{I}_{2}}+\,{{({{I}_{2}}{{\omega }_{2}})}^{2}}}{2({{I}_{1}}+{{I}_{2}})}\]
D) None of these
Correct Answer: C
Solution :
Conservation of angular momentum \[{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}=({{I}_{1}}+{{I}_{2}})\omega \] Angular velocity of system\[\omega =\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\] \[\therefore \]Rotational kinetic energy\[=\frac{1}{2}({{I}_{1}}+{{I}_{2}}){{\omega }^{2}}\] \[=\frac{1}{2}({{I}_{1}}+{{I}_{2}}){{\left( \frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}} \right)}^{2}}\] \[=\frac{{{({{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}})}^{2}}}{2({{I}_{1}}+{{I}_{2}})}\]You need to login to perform this action.
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