Kinematics Question 543
Question: A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg it’s tied to it and it’s revolved in a circular path of radius 2 m in a vertical plane. If $ g=10m/s^{2} $ , then the maximum angular velocity of the stone will be[MP PMT 1994]
Options:
A) $ 5rad/s $
B)$ \sqrt{30}rad/s $
C) $ \sqrt{60}rad/s $
D)$ 10rad/s $
Show Answer
Answer:
Correct Answer: A
Solution:
$ T _{\max }=m\omega _{^{\max }}^{2}r+mg $
therefore $ \frac{T _{\max }}{m}={{\omega }^{2}}r+g $
therefore $ \frac{30}{0.5}-10={{\omega }^{2}} _{\max }r $
therefore $ {\omega _{\max }}=\sqrt{\frac{50}{r}}=\sqrt{\frac{50}{2}}=5rad/s $
