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

Show Answer

Answer:

Correct Answer: B

Solution:

$ |\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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