A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
- [NEET 2016]
- A
$\sqrt {\frac{{{m_1} + {m_2}}}{{{m_2}}}} $
- B
$\;\sqrt {\frac{{{m_2}}}{{{m_1}}}} $
- C
$\;\sqrt {\frac{{{m_1} + {m_2}}}{{{m_1}}}} $
- D
$\;\sqrt {\frac{{{m_1}}}{{{m_2}}}} $
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- [IIT 2023]