NEET Solved Paper 2016 Question 10
Question: A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass $ m _2 $ is attached to the free end of the rope. A transverse pulse of wavelength $ {\lambda_1} $ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $ {\lambda_2}. $ The ratio $ {\lambda_2}/{\lambda_1} $ is :
Options:
A) $ \sqrt{\frac{m _1}{m _2}} $
B) $ \sqrt{\frac{m _1+m _2}{m _2}} $
C) $ \sqrt{\frac{m _2}{m _1}} $
D) $ \sqrt{\frac{m _1+m _2}{m _1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ T _1=m _2g $ $ T _2=(m _1+m _2)g $ $ Velocity\propto \sqrt{T} $ $ \lambda \propto \sqrt{T} $ $ \frac{{\lambda_1}}{{\lambda_2}}=\frac{\sqrt{T _1}}{\sqrt{T _2}} $
$ \Rightarrow $ $ \frac{{\lambda_2}}{{\lambda_1}}=\sqrt{\frac{m _1+m _2}{m _2}} $
