A) \[\frac{1}{2}m{{K}^{2}}{{\omega }^{2}}\]
B) \[\frac{1}{2}m{{a}^{2}}{{\omega }^{2}}\]
C) \[\frac{1}{2}m(a+{{K}^{2}}){{\omega }^{2}}\]
D) \[\frac{1}{2}m({{a}^{2}}+{{K}^{2}}){{\omega }^{2}}\]
Correct Answer: D
Solution :
MI of body about centre of mass \[{{I}_{cm}}=m{{k}^{2}}\] MI of body about new parallel axis \[{{I}_{new}}{{I}_{cm}}+m{{a}^{2}}\] \[=m{{k}^{2}}+m{{a}^{2}}\] \[=m\,({{K}^{2}}+{{a}^{2}})\] \[\therefore \] Kinetic energy, \[K=\frac{1}{2}{{I}_{new}}{{\omega }^{2}}\] \[=\frac{1}{2}\,m({{K}^{2}}+{{a}^{2}}){{\omega }^{2}}\]
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