A metal wire of density ' $e$ ' floats on water surface horizontally. If it is NOT to sink in water, then…

A metal wire of density ' $e$ ' floats on water surface horizontally. If it is NOT to sink in water, then maximum radius of wire is ( $\mathrm{T}$ = surface tension of water, $\mathrm{g}$ = gravitational acceleration)
  1. $\frac{\pi \mathrm{eg}}{\mathrm{T}}$
  2. $\frac{\mathrm{T}}{\pi \mathrm{eg}}$
  3. $\sqrt{\frac{2 \mathrm{~T}}{\pi \mathrm{eg}}}$
  4. $\sqrt{\frac{\pi e g}{T}}$

Solution

The correct option is (C). There are two free surfaces as shown in the figure: Consider the force balance per unit length as shown in the diagram above: $2 \mathrm{~T}=\mathrm{e} \pi \mathrm{r}^2 \mathrm{~g}$ Therefore, $r=\sqrt{\frac{2 \mathrm{~T}}{\pi \mathrm{eg}}}$. We neglect buoyancy force as it is negligible as compared to surface tension force!

Asked in: MHT CET 2022 (05 Aug Shift 1)

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