Physics Two Dimensional Motion Question 105
Question: When a ceiling fan is switched off its 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
BETA
