A) \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\]
B) \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]
C) \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]
D) \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\]
Correct Answer: C
Solution :
[c] \[{{T}_{west}}=\frac{2\pi R}{{{v}_{0}}+R\omega }\] and \[{{T}_{east}}=\frac{2\pi R}{{{v}_{0}}-R\omega }\Rightarrow \Delta T={{T}_{east}}\] \[\Rightarrow {{T}_{east}}-{{T}_{west}}=2\pi R\left[ \frac{2\pi R}{{{v}^{2}}_{0}-{{R}^{2}}{{\omega }^{2}}} \right]=\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]You need to login to perform this action.
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