MHT CET · Physics · Mechanical Properties of Fluids
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)
- A \(\frac{\pi \mathrm{eg}}{\mathrm{T}}\)
- B \(\frac{\mathrm{T}}{\pi \mathrm{eg}}\)
- C \(\sqrt{\frac{2 \mathrm{~T}}{\pi \mathrm{eg}}}\)
- D \(\sqrt{\frac{\pi e g}{T}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{2 \mathrm{~T}}{\pi \mathrm{eg}}}\)
Step-by-step Solution
Detailed explanation
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!
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!
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