Buoyant force $\left(F_b\right)=1 \times \frac{4}{3} \pi\left(\frac{D^3}{8}\right) \cdot g$
For Just Float $\Rightarrow \mathrm{W}=\mathrm{F}_{\mathrm{b}}$
$\Rightarrow\left(\mathrm{D}^3-\mathrm{d}^3\right) \sigma=\mathrm{D}^3$
$\Rightarrow 1-\frac{\mathrm{d}^3}{\mathrm{D}^3}=\frac{1}{\sigma}$
$\Rightarrow 1-\frac{1}{\sigma}=\left(\frac{\mathrm{d}}{\mathrm{D}}\right)^3$
$\Rightarrow\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}=\left(\frac{\mathrm{D}}{\mathrm{d}}\right)$
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| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
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