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 mFrom 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, v∝√T So, v1v2=√T1T2 ..........(1) Also, v=λf For the same source, v∝λ 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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