\(\frac{1}{{2L}}\sqrt {\frac{T}{m}} = \frac{v}{{4L}}\)…..\((i) \)
and \(\frac{1}{{2L}}\sqrt {\frac{{T + 8}}{m}} = \frac{{3v}}{{4L}}\) ..…\((ii)\)
Dividing equation \((i)\) and \((ii),\) \(\sqrt {\frac{T}{{T + 8}}} = \frac{1}{3} \Rightarrow T = 1N\)