A) \[8.5\,\,s\]
B) \[5\,\,s\]
C) \[2\,\,s\]
D) \[1\,\,s\]
Correct Answer: C
Solution :
Key Idea: Kinetic energy of rotation is half the product of the moment of inertia \[\left( \text{I} \right)\] of the body and the square of the angular velocity \[\left( \omega \right)\] of the body. Kinetic energy of rotation \[=\frac{1}{2}\times \] moment of inertia \[\times \]angular velocity. \[i.e.\,,\] \[K=\frac{1}{2}I{{\omega }^{2}}\] \[\Rightarrow \] \[{{\omega }^{2}}=\frac{2K}{I}\] Given, \[I=1.2\,kg{{m}^{2}}\], \[K=1500\,\,J\] \[{{\omega }^{2}}=\frac{2\times 1500\,}{1.2}\] \[{{\omega }^{2}}=2500\] \[\Rightarrow \] \[{{\omega }^{2}}=50\,\,rad/s\] From the equation of angular motion, we have \[\omega ={{\omega }_{0}}+a\,t\] Where \[{{\omega }_{0}}\] is initial angular velocity, \[\alpha \]is angular acceleration and t is time. Given, \[{{\omega }_{0}}=0,\,\,\omega =50\,\,rad/s,\,\,a=25\,rad/{{s}^{2}}\] \[\therefore \] \[t=\frac{\omega }{a}=\frac{50}{25}=2s\] Note: The equation of kinetic energy of rotation is similar to kinetic energy expression in linear from\[\left( \frac{1}{2}m{{v}^{2}} \right)\] and equation of angular motion is similar to Newton?s equation of motion\[\left( v=u+at \right)\].
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