wave_mechanics critical_thinking Question 36
Question: A wire of $ 9.8\times {{10}^{-3}}kg{{m}^{-1}} $ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of 30° with the horizontal. Masses m and M are tied at the two ends of wire such that m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of 100 ms?1. Chose the correct option
Options:
A) $ m=20kg $
B) $ m=5kg $
C) $ m=2kg $
D) $ m=7kg $
Show Answer
Answer:
Correct Answer: A
Solution:
$ v=\sqrt{\frac{T}{\mu }} $ For equilibrium $ Mg=mg\sin 30=T $
Therefore $ M=\frac{m}{2} $
Therefore $ 100=\sqrt{\frac{Mg}{9.8\times {{10}^{-3}}}}=\sqrt{\frac{M(9.8)}{9.8\times {{10}^{-3}}}} $
Therefore $ 100=\sqrt{M(1000)} $
Therefore $ M=10kg $ and $ m=20kg $
BETA
