A) \[{{V}_{A}}-{{V}_{E}}=\frac{9}{2}B\omega {{l}^{2}}\]
B) \[{{V}_{E}}-{{V}_{A}}=\frac{9}{2}B\omega {{l}^{2}}\]
C) \[{{V}_{D}}-{{V}_{E}}=\frac{B\omega {{l}^{2}}}{2}\]
D) \[{{V}_{A}}-{{V}_{E}}=4B\omega {{l}^{2}}\]
Correct Answer: D
Solution :
Since, \[{{v}_{E}}-{{v}_{D}}=\frac{\Beta \omega l}{2}\times l\] \[{{v}_{E}}-{{v}_{D}}=\frac{B\omega {{l}^{2}}}{2}\] ? (i) \[{{v}_{E}}-{{v}_{A}}=\frac{B\omega 3l}{2}\times 3l=\frac{9B\omega {{l}^{2}}}{2}\] ? (ii) Subtracting Eq.(i) from Eq. (ii), we get. \[{{v}_{A}}-{{v}_{E}}=4B\omega {{l}^{2}}\] \[\Rightarrow \]\[{{v}_{A}}>{{v}_{E}}\]
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