A) \[m{{k}^{2}}{{r}^{2}}{{t}^{2}}\]
B) \[m{{k}^{2}}{{r}^{2}}t\]
C) \[\pi m{{k}^{2}}{{r}^{2}}{{t}^{2}}\]
D) \[m{{k}^{4}}{{r}^{2}}t\]
Correct Answer: D
Solution :
: Acceleration \[{{a}_{c}}={{k}^{4}}r{{t}^{2}}\] centripetal acceleration \[=\frac{{{v}^{2}}}{r}\] \[\therefore \]\[\frac{{{v}^{2}}}{r}={{k}^{4}}r{{t}^{2}}\] or\[{{v}^{2}}={{k}^{4}}{{r}^{2}}{{t}^{2}}\] From Work - Energy theorem, \[W=\frac{1}{2}m{{v}^{2}}\] \[\therefore \]\[W=\frac{1}{2}m\times {{k}^{4}}{{r}^{2}}{{t}^{2}}\] \[\therefore \]\[\frac{dW}{dt}=\frac{2m{{k}^{4}}{{r}^{2}}t}{2}\] Power \[=m{{k}^{4}}{{r}^{2}}t\].
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