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)x to the power of 0
(b)square root of x
(c)bevelled fraction numerator 1 over denominator square root of x end fraction
(d)X

Asked by Akanksha Mishra | 20th Mar, 2015, 03:35: PM

Expert Answer:

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)

Answered by Romal Bhansali | 20th Mar, 2015, 06:28: PM