Kinematics Question 452
Question: A vector $ \vec{a} $ it’s turned without a change in it’s length through a small angle $ d\theta $ . The value of $ |\Delta \vec{a}| $ and $ \Delta a $ are respectively
Options:
A) $ 0,ad\theta $
B) $ a,d\theta ,0 $
C) 0, 0
D) None of these
Correct Answer: D [d] $ |\Delta \vec{a}|=\sqrt{a^{2}+a^{2}-2.a.a.\cos (d\theta )} $
$ =2a\sin ( \frac{d\theta }{2} ) $ For small angle
$ \sin \frac{d\theta }{2}\approx \frac{d\theta }{2} $ $ \therefore $ $ |\Delta \vec{a}|=2a\times \frac{d\theta }{2}=a.d\theta $
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