KVPY 2019 SB SX Exam Previous Papers

Question : 96 of 120

Marks: +1, -0

A rope of length L and uniform linear density is hanging from the ceiling. A transverse wave pule, generated close to the free end of the rope, travels upwards through the rope. Select the correct option

The speed of the pulse decreases as it moves up
The time taken by the pulse to travel the length of the rope is proportional to $√L$
The tension will be constant along the length of the rope.
The speed of the pulse will be constant along the length of the rope

Validate

Solution:

V=√{T/µ}=√{{µ×g}/µ}=√{xg}

here x = distance from lower end
Now

v^2 = gx ⇒ v^2 =0^2+ 2ax

⇒ u = 0 and a = g/2 (constant)
so

t=√{{2x}/a}⇒\Total \time t ∝ √ L

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