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