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