Kinematics Question 536
Question: A wheel it’s subjected to uniform angular acceleration about it’s axis. Initially it’s angular velocity is zero. In the first 2 sec, it rotates through an angle $ {\theta _{1}} $ . In the next 2 sec, it rotates through an additional angle $ {\theta _{2}} $ . The ratio of $ \sqrt{3}mg $ it’s[AIIMS 1985]
Options:
A) 1
B)2
C) 3
D) 5
Show Answer
Answer:
Correct Answer: C
Solution:
Using relation $ \theta ={\omega _{0}}t+\frac{1}{2}at^{2} $
$ {\theta _{1}}=\frac{1}{2}(\alpha ){{(2)}^{2}}=2\alpha $ -(i)(As $ {\omega _{0}}=0,t=2\sec $ )
Now using same equation for t = 4 sec, w0 = 0 $ {\theta _{1}}+{\theta _{2}}=\frac{1}{2}\alpha {{(4)}^{2}}=8\alpha $ -(ii) From (i) and (ii),$ {\theta _{1}}=2\alpha $
and $ {\theta _{2}}=6\alpha $ $ \frac{{\theta _{2}}}{{\theta _{1}}}=3 $
