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QJEEM20Phcd76: JEE Main 2020 Physics - Class 11 JEEM20Phcd76 Solution: A uniform thin rope of length 12 m and mass 6 kg hangs…

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?

Multiple Choice Options

  • A 12
  • B 3
  • C 9
  • D 6

Step-by-Step Verified Solution

JEE Main 2020 (Online) 3rd September Morning Slot Physics - Waves Question 72 English Explanation

T1 = 2g

T2 = 8g

V = Tμ\sqrt {{T \over \mu }}

∴\therefore V ∝\propto T\sqrt T

Also V = f λ\lambda

∴\therefore V1 = f1 λ\lambda 1

and V2 = f2 λ\lambda 2

We know frequency of sources are same.

∴\therefore f1 = f2

So T1T2=λ1λ2\sqrt {{{{T_1}} \over {{T_2}}}} = {{{\lambda _1}} \over {{\lambda _2}}}

⇒\Rightarrow 2g8g=6λ2\sqrt {{{2g} \over {8g}}} = {6 \over {{\lambda _2}}}

⇒\Rightarrow λ\lambda 2 = 12 cm

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