A) 2\[\omega \]
B) 4\[\omega \]
C) 6\[\omega \]
D) 8\[\omega \]
Correct Answer: D
Solution :
When no external torque is acting upon a body rotating about an axis, then angular momentum of the body remains constant. Therefore, \[J=I\omega =\] constant where \[I=m{{r}^{2}}\] (moment of inertia) \[\therefore \] \[{{m}_{1}}r_{1}^{2}\omega ={{m}_{2}}r_{2}^{2}\,{{\omega }_{2}}\] \[\Rightarrow \] \[{{\omega }_{2}}=\frac{{{m}_{1}}\,r_{1}^{2}\,{{\omega }_{1}}}{{{m}_{2}}\,r_{2}^{2}}\] Given, \[{{m}_{1}}=m\], \[{{r}_{1}}=r\], \[{{\omega }_{1}}=2\omega \] \[{{m}_{2}}=m,\,{{r}_{2}}=\frac{r}{2}\] \[\therefore \] \[{{\omega }_{2}}=\frac{m{{r}^{2}}(2\,\omega )}{m\,{{(r/2)}^{2}}}=\frac{m{{r}^{2}}}{m{{r}^{2}}}8\omega \] \[\Rightarrow \] \[{{\omega }_{2}}=8\omega \]You need to login to perform this action.
You will be redirected in
3 sec