A) \[2|\psi ||\cos \phi /4|\]
B) \[|\psi ||\sin \phi /4|\]
C) \[|\psi {{|}^{2}}|\sin \phi /4{{|}^{2}}\]
D) \[2|\psi ||\sin \phi /4|\]
Correct Answer: D
Solution :
Let \[\psi \] is rotated through angle \[\frac{\phi }{2}\] to get\[\eta \]. \[\therefore \]\[|\psi |=|\eta |\]and angle between \[\psi \] and \[\eta \] is \[\phi /2\]. \[\therefore \]Magnitude of the change in vector \[\psi \] is \[|\eta -\psi |=\sqrt{|\eta {{|}^{2}}+|\psi {{|}^{2}}+2|\eta ||\psi |\cos \left( \pi -\frac{\phi }{2} \right)}\] \[=|\psi |\sqrt{2(1-\cos \phi /2)}\] \[=|\psi |\times \sqrt{2\times 2{{\sin }^{2}}\phi /4}\] \[=|\psi |\times 2sin\phi /4=2|\psi ||sin\phi /4|\]
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