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Q.

A bowl whose bottom has round holes of diameter 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height (in cm) up to which water can be filled in the vessel without leakage. (Given, surface tension of water = 75 x 10-3 Nm-l , g=10 ms-2 and density of water = 1 g/cm3.

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answer is 3.

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Detailed Solution

The vertical force due to surface at the hole=Tcos⁡θ×L=Tcos⁡θ×2πr This will balance weight mg=πr2hρg∴ Tcos⁡θ×2πr=πr2hρg⇒ h=2Tcos⁡θrρgh is maximum, when cos⁡θ=1∴ hmax=2Trρg=2×0.0750.0005×1000×10=0.03m=3cm
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