A light string is tied at one end to a fixed support and to a heavy string of equal length $\mathrm{L}$ at the other end $\mathrm{A}$ as shown in the figure ( Total length of both strings combined is $2\mathrm{L}$). A block of mass $\mathrm{M}$ is tied to the free end of heavy string. Mass per unit length of the strings are $\mathrm{\mu }$ and $16\mathrm{\mu }$ and tension is $\mathrm{T}$. Find lowest positive value of frequency such that junction point $\mathrm{A}$ is a node.

• A

  $\frac{1}{\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$
• B

  $\frac{5}{2\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$
• C

  $\frac{3}{2\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$
• Correct answer
  D

  $\frac{1}{2\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$

Hence, the correct answer is option: 'D'.