Explanation

(c) Given,
$\frac{T_{A}}{T_{B}} = 1,\frac{L_{A}}{L_{B}} = \frac{80}{x}$
$\frac{D_{A}}{D_{B}} = \frac{2}{1},\frac{d_{A}}{d_{B}} = \frac{0.81}{1}$
Let $\mu_{1}and\ \mu_{2}$ be the linear densities.
$\therefore\frac{\mu_{A}}{\mu_{B}} = \left( \frac{D_{A}}{D_{B}} \right)^{2} \times \frac{d_{A}}{d_{B}}$
$= \left( \frac{2}{1} \right)^{2} \times 0.81$
=4×0.81=3.24
$\therefore\ \ \ \frac{v_{1}}{v_{2}} = \frac{L_{B}}{L_{A}} \times \sqrt{\frac{T_{A}}{T_{B}} \times \frac{\mu_{B}}{\mu_{A}}}$
$1 = \frac{x}{80} \times \sqrt{1 \times \frac{1}{3.21}}\ $
or x=144