A) \[2m\text{ }{{s}^{-1}}\]
B) \[1m\text{ }{{s}^{-1}}\]
C) \[1.5m{{s}^{-1}}\]
D) \[0.5m{{s}^{-1}}\]
Correct Answer: B
Solution :
:Here, Moment of inertia of the body about its axis of rotation, \[I=3\text{ }kg\,{{m}^{2}}\] Angular velocity of rotation, \[\omega =3\text{ }rad\text{ }{{s}^{-1}}\] Kinetic energy of rotation of the body is \[{{K}_{R}}=\frac{1}{2}I{{\omega }^{2}}\] Kinetic energy of body of mass m(= 27kg) moving with velocity v is \[{{K}_{T}}=\frac{1}{2}m{{v}^{2}}\] As per question, \[{{K}_{R}}={{K}_{T}}\] \[\therefore \] \[\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}m{{v}^{2}}\] \[\frac{1}{2}\times 3\times {{3}^{2}}=\frac{1}{2}\times 27\times {{v}^{2}}\] or \[{{v}^{2}}=1\] or \[v=1\,m\,{{s}^{-1}}\]
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