A) \[\frac{(M+4m)\,\omega }{M}\]
B) \[\frac{(M-4m)\,\omega }{M+4m}\]
C) \[\frac{M\,\omega }{4m}\]
D) \[\frac{M\,\omega }{M+4m}\]
Correct Answer: D
Solution :
Key Idea: If external torque acting on the system is zero, hence angular momentum remains conserved. |
\[{{\tau }_{\text{ext}}}=0\] |
or \[\frac{dL}{dt}=0\] |
or \[L=\]constant |
or \[I\omega =\] constant |
\[\therefore \] \[{{I}_{1}}\,{{\omega }_{1}}={{I}_{2}}\,{{\omega }_{2}}\] (i) |
Here, \[{{I}_{1}}=M{{r}^{2}},\,\,{{\omega }_{1}}=\omega ,\,\,{{I}_{2}}=M{{r}^{2}}+4m{{r}^{2}}\] |
Hence, Eq. (i) can be written as |
\[M{{r}^{2}}\omega =(M{{r}^{2}}+4m{{r}^{2}})\,{{\omega }_{2}}\] |
\[\therefore \] \[{{\omega }_{2}}=\frac{M\omega }{M+4m}\] |
You need to login to perform this action.
You will be redirected in
3 sec