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



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