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Question

A uniform rope of length 10 m and mass 15 kg hangs vertically from a rigid support. A block of mass 5 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.08 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope will be
(Take g=10 m/s2)


A
0.36 m
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B
0.26 m
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C
0.16 m
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D
0.06 m
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Solution

The correct option is C 0.16 m
From FBD of block,

Applying equilibrium condition, tension in the rope at lower end,
T1=50 N
Similarly, tension in the rope at the top end,
T2=50+150=200 N


Velocity of wave pulse,
v=Tμ
For the same rope,
vT
So, v1v2=T1T2 ..........(1)
Also, v=λf
For the same source,
vλ
So, v1v2=λ1λ2 ..........(2)
From (1) and (2),
λ1λ2=T1T2
0.08λ2=50200
λ2=0.16 m
Why this question?
Tips: Once the wave pulse is generated then the associated momentum and energy changes due to interaction of the wave with particles of the medium. However, frequency remains unchanged.

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