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JEE Main 20203 SeptemberMorning Shift

Exam: JEE Main
Year: 2020
Date: 3 September
Shift: Morning Shift
Subject: Physics
Chapter: Waves and Sound

JEE Main 2020 · 3 September · Morning Shift · Physics · Waves and Sound

A uniform thin rope of length 12m and mass 6kg hangs vertically...

A uniform thin rope of length

12m

and mass

6kg

hangs vertically from a rigid support and a block of mass

2kg

is attached to its free end. A transverse short wave train of wavelength

6cm

is produced at the lower and the rope. What is the wavelength of the wave train (in

cm

) when it reaches the top of the rope?

Options

A $3$
B $6$
C $12$
D $9$

Correct answer

C. $12$

Step-by-step solution

$V = f \lambda$

$\dfrac{V1}{\lambda1} = \dfrac{V2}{\lambda2}$

${λ}_{2} = \dfrac{V2}{V1}{λ}_{1} = \sqrt{\dfrac{T2}{T1}}{λ}_{1}{T}_{2} = 8g \left(Top\right)$

$\sqrt{\dfrac{8g}{2g}}{λ}_{1}$

${T}_{1} = 2g\left(Bottom\right)= 2{λ}_{1} = 12cm$

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