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) \[\frac{{{({{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}})}^{2}}}{2({{I}_{1}}+{{I}_{2}})}\]
D) None of these
Correct Answer: C
Solution :
By the law of conservation of angular momentum: Angular velocity of system, \[\omega =\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\] 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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