Kinematics Question 110
Question: A vector $ \overrightarrow{a} $ it’s turned without a change in it’s length through a small angle $ d\theta . $ The value of $ |\Delta \overrightarrow{a}| $ and $ \Delta a $ are respectively
Options:
A) $ 0,ad\theta $
B) $ ad\theta ,0 $
C) 0, 0
D) None of these
Correct Answer: B $ |\overrightarrow{OA}|=a $ and $ |\overrightarrow{OB}|=a $ Also from triangle rule $ \overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{AB}=\Delta \overrightarrow{a} $ $ \Rightarrow |\Delta \overrightarrow{a}|=AB $ Using angle $ =\frac{arc}{radius} $ therefore AB = a . dq So $ |\Delta \overrightarrow{a}|=ad\theta $ $ \Delta a $ means change in magnitude of vector i.e. $ |\overrightarrow{OB}|-|\overrightarrow{OA}| $ $ \Rightarrow a-a=0 $ So $ \Delta a=0 $
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