Is the Answer Correct? Dipping a Cylinder w/ Small Hole in Liquid

AI Thread Summary
The discussion revolves around the maximum depth a cylindrical vessel with a small hole can be submerged in a liquid before it fills with liquid, given the formula √(2S/rdg) for the maximum depth. Participants express differing opinions on the correctness of the formula, with some asserting that it seems accurate while others challenge the presence of the square root, questioning the dimensional consistency of the equation. The debate highlights confusion regarding how the square root factor is derived in this context. Ultimately, the discussion emphasizes the need for clarity on the underlying physics and mathematics involved in the problem. The correctness of the provided answer remains contested.
dk_ch
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An empty cylindrical vessel with a small circular hole of radius r at the bottom is dipped vertically in a liquid of density d keeping the bottom downward. At what maximum depth can it be dipped before the liquid enters into it? The surface tension of the liquid is S. The answer given in the text is √(2S/rdg). Is the answer correct?
 
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dk_ch said:
An empty cylindrical vessel with a small circular hole of radius r at the bottom is dipped vertically in a liquid of density d keeping the bottom downward. At what maximum depth can it be dipped before the liquid enters into it? The surface tension of the liquid is S. The answer given in the text is √(2S/rdg). Is the answer correct?


It seems correct to me.
 
sankalpmittal said:
It seems correct to me.

Sir will u please explain How?
How does square root arise here?
 
dk_ch said:
Sir will u please explain How?
How does square root arise here?


Square root. Then it is wrong. Please check the dimensions. Dimensions are consistent if there were no square root.
 
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