Question
Fri March 20, 2015 By: Akanksha Mishra

A rope of length L and mass m hangs freely from the ceiling.The velocity of transverse  as a function of position x along the rope is proportional to
 
(a)A rope of length L and mass m hangs freely from the ceiling, Question no 89383, Physics
(b)A rope of length L and mass m hangs freely from the ceiling, Question no 89383, Physics
(c)A rope of length L and mass m hangs freely from the ceiling, Question no 89383, Physics
(d)X

Expert Reply
Romal Bhansali
Fri March 20, 2015
The velocity of transverse wave on a rope is given as
 
begin mathsize 14px style straight v equals square root of straight T over straight mu end root end style
Now, when the rope is hanging, the tension in the string depends on the position x along the rope.
 
T = μgx
 
Hence, we have
 
begin mathsize 14px style straight v equals square root of μgx over straight mu end root equals square root of gx end style
Hence, the correct option is (b)
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