c
\(T \cos \theta=\mathrm{mg}\)

\(\mathrm{T} \sin \theta=\mathrm{F}_{\mathrm{e}}\)

\(\tan \theta=\frac{\mathrm{Fe}_{\mathrm{e}}}{\mathrm{mg}}\)

\(\tan \theta=\frac{F_e}{\rho_B V g}\)      \(....(I)\)

\(\tan \theta=\frac{F_e}{\frac{k}{\left(\rho_B-\rho_{\mathrm{L}}\right) V g}}\)        \(....(ii)\)

\(\text { From Eq. (i) & (ii) }\)

\(\rho_{\mathrm{B}} \mathrm{Vg}=\left(\rho_{\mathrm{B}}-\rho_{\mathrm{L}}\right) \mathrm{kVg}\)

\(1.4=0.7 \mathrm{k}\)

\(\mathrm{k}=2\)