A) 250 J
B) 0.25 J
C) 2500 J
D) 2.5 J
Correct Answer: A
Solution :
Given: \[{{K}_{rot}}\]= 2.5 J, \[{{\omega }_{1}}\]= \[\omega ,\]\[{{\omega }_{2}}\] = 10 \[\omega \] Rotational kinetic energy \[{{K}_{rot}}=\frac{1}{2}I{{\omega }^{2}}\] or \[{{K}_{rot}}\propto {{\omega }^{2}}\] \[\therefore \] \[\frac{K{{}_{rot}}}{K{{}_{rot}}}={{\left( \frac{{{\omega }_{2}}}{{{\omega }_{1}}} \right)}^{2}}={{(10)}^{2}}=100\] \[\therefore \] \[K{{}_{rot}}=100\times 2.5=250\,\text{J}\]
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