A) \[2r\,d\cos \left( \frac{\theta }{2} \right)\]
B) \[2r\,\cot \left( \frac{\theta }{2} \right)\]
C) \[2r\,\tan \left( \frac{\theta }{2} \right)\]
D) \[2r\,\sin \left( \frac{\theta }{2} \right)\]
Correct Answer: D
Solution :
In \[\Delta AOB\,\]\[\sin \frac{\theta }{2}=\frac{AB}{AO}\] \[(\because \,AO=r)\] \[AB=AO\,\,\sin \frac{\theta }{2}\Rightarrow AB=r\sin \frac{\theta }{2}\] \[AC=AB+BC\] \[(\because \,AB=BC)\] \[=r\sin \frac{\theta }{2}+r\sin \frac{\,\theta }{2}\] \[AC=2r\sin \frac{\theta }{2}\] So, the magnitude of the corresponding linear displacement will be \[\sin \frac{\theta }{2}.\]You need to login to perform this action.
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