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A rope of uniform mass M and length L hangs from the branch of a tree.Find the tension at a distance x from the ground.

A rope of uniform mass M and length L hangs from the branch of a tree.Find the tension at a distance x from the ground.

Grade:11

2 Answers

Aman Bansal
592 Points
9 years ago

Dear Rahul,

mass of thr rope is m
length of the rope is L .
Then mass per unit length is μ = m/L
then tension at distance y  is T = m''g
m'' = mass of the part having length y = μy
then tension T =  μy*g
then speed of transverse wave is v = √T/μ =√μy*g /μ  = √(gy)
b) distance travelled by the transverse wave is s = L
   velocity of wave at the bottomis u = 0
   velocity of the wave at the top is v =√gL
  Then distance s = average velocity *time
      L =[ (v+u)/2]*t
        = [ (√gL)/2]*t
then time t = 2√g/L

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Rahul Nath.R
18 Points
9 years ago

But the answer to this question in the book is tension =0 at the height x from the ground.

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