A) \[35.32\,\text{rad/sec}\]
B) \[28.16\,\text{rad/sec}\]
C) \[14-08\,\text{rad/sec}\]
D) \[7\,\text{rad/sec}\]
Correct Answer: B
Solution :
Mass\[m=2\,kg\] Initial radius of the path \[{{r}_{1}}=0.8\,m\]Initial angular velocity \[{{\omega }_{1}}=44\,\text{rad/sec}\] Final radius of the path \[{{r}_{2}}=1\,m\] The moment of inertia of rotating body is given by \[{{I}_{1}}={{m}_{1}}r_{1}^{2}=2\times {{(0.8)}^{2}}=1.28\,kg-{{m}^{2}}\] Similarly,\[{{I}_{2}}=mr_{2}^{2}=2\times {{(1)}^{2}}=2kg-{{m}^{2}}\] Now from the law of conservation of angular momentum is \[{{I}_{1}}{{\omega }_{1}}={{I}_{2}}{{\omega }_{2}}\] \[{{\omega }_{2}}=\frac{{{I}_{1}}}{{{I}_{2}}}\times {{\omega }_{1}}\] \[=\frac{1.28}{2}\times 44=28.16\,\text{rad/sec}\]
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