A) \[\frac{{{I}_{1}}{{I}_{2}}{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}}{2({{I}_{1}}+{{I}_{2}})}\]
B) \[\frac{{{I}_{1}}{{I}_{2}}{{(\omega _{1}^{2}-\omega _{2}^{2})}^{2}}}{2({{I}_{1}}+{{I}_{2}})}\]
C) \[\frac{2{{I}_{1}}{{I}_{2}}{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}}{({{I}_{1}}+{{I}_{2}})}\]
D) \[\frac{{{I}_{1}}\omega _{1}^{2}-{{I}_{2}}\omega _{2}^{2}}{({{I}_{1}}+{{I}_{2}})}\]
Correct Answer: A
Solution :
\[\Delta KE=\frac{1}{2}({{I}_{1}}\omega _{1}^{2}-{{I}_{2}}\omega _{2}^{2})-\frac{1}{2}({{I}_{1}}\omega '_{1}^{2}-{{I}_{2}}\omega '_{2}^{2})\] For momentum balance, \[{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}={{I}_{1}}\omega {{'}_{1}}+{{I}_{2}}\omega {{'}_{2}}\] \[=\omega {{'}_{1}}=\omega {{'}_{2}}=\frac{{{I}_{1}}{{\omega }_{1}}+{{I}_{2}}{{\omega }_{2}}}{{{I}_{1}}+{{I}_{2}}}\] \[\Delta KE=\frac{{{I}_{1}}{{I}_{2}}}{2({{I}_{1}}+{{I}_{2}})}{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}\]You need to login to perform this action.
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