A) \[\frac{\pi \ell }{12}\]
B) \[\frac{\ell }{2}\left( 1+\frac{\pi }{12} \right)\]
C) \[\frac{\ell }{2}\left( 1-\frac{\pi }{6} \right)\]
D) \[\frac{\ell }{2}\left( 1+\frac{\pi }{6} \right)\]
Correct Answer: D
Solution :
As torque = change om angular momentum |
\[\therefore F,\,\,\Delta t=mv\] (Linear)... (1) |
and \[\left( F.\frac{\ell }{2} \right)\Delta t=\frac{m{{\ell }^{2}}}{12}.\omega \] (angular)...(2) |
Dividing: (1) and (2) |
\[2=\frac{12v}{\omega \ell }\Rightarrow \,\,\,\,\,\,\,\,\,\omega =\frac{6v}{\ell }\] |
Using : S = ut: |
Displacement of COM is: \[\frac{\pi }{2}=\omega t=\left( \frac{6v}{\ell } \right)t\] |
and \[x=vt\] |
Dividing: \[\frac{2x}{\pi }=\frac{\ell }{6}\] \[\Rightarrow \,\,\,\,x=\frac{\pi \ell }{12}\]\[\Rightarrow \] Coordination of A will be \[\left[ \frac{\pi \ell }{12}+\frac{\ell }{2},0 \right]\] |
Hence [D]. |
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