Kinematics Question 557
Question: When a ceiling fan is switched off it’s angular velocity reduces to 50% while it makes 36 rotations.How many more rotation will it make before coming to rest (Assume uniform angular retardation)[KCET 2001]
Options:
A) 18
B)12
C) 36
D) 48
Show Answer
Answer:
Correct Answer: B
Solution:
By using equation$ {{\omega }^{2}}=\omega _{0}^{2}-2\alpha \theta $
$ {{( \frac{{\omega _{0}}}{2} )}^{2}}=\omega _{0}^{2}-2\alpha (2\pi n) $
therefore $ \alpha =\frac{3}{4}\frac{\omega _{0}^{2}}{4\pi \times 36} $ , (n = 36) ..(i)
Now let fan completes total n¢ revolution from the starting to come to rest $ 0=\omega _{0}^{2}-2\alpha (2\pi {n}’) $
therefore $ {n}’=\frac{\omega _{0}^{2}}{4\alpha \pi } $
substituting the value of a from equation (i) $ {n}’=\frac{\omega _{0}^{2}}{4\pi }\frac{4\times 4\pi \times 36}{3\omega _{0}^{2}}=48 $
revolution Number of rotation = 48 - 36 = 12
