A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength \lambda1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \lambda2. The ratio \lambda2/\lambda1 is:

  • Option 1)

    \sqrt{\frac{\text{m}_{1}}{\text{m}_{2}}}

  • Option 2)

    \sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{2}}}

  • Option 3)

    \sqrt{\frac{\text{m}_{2}}{\text{m}_{1}}}

  • Option 4)

    \sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{1}}}

 

Answers (1)

As we discussed in

Speed of wave on string -

v= sqrt{frac{T}{mu }}
 

- wherein

T= Tension in the string

mu = linear mass density

 

 T1 = m2g

T2 = ( m+ m) g

V \alpha \sqrt{T}

\lambda\: \alpha \sqrt{T}

\therefore \frac{\lambda _{1}}{\lambda _{2}}=\frac{\sqrt{T_{1}}}{\sqrt{T_{2}}} \Rightarrow \frac{\lambda _{1}}{\lambda _{2}}= \frac{\sqrt{m_{1}+ m_{2}}}{\sqrt{m_{2}}}

\sqrt{\frac{m_{1}+m_{2}}{m_{2}}}


Option 1)

\sqrt{\frac{\text{m}_{1}}{\text{m}_{2}}}

This option is incorrect

Option 2)

\sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{2}}}

This option is correct

Option 3)

\sqrt{\frac{\text{m}_{2}}{\text{m}_{1}}}

This option is incorrect

Option 4)

\sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{1}}}

This option is incorrect

Preparation Products

Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout NEET May 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 4999/-
Buy Now
Knockout NEET May 2022 (Subscription)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 5499/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions