JEE Mains · Physics · STD 11 - 9.1 fluid mechanics
Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\)
- A \(5.1\)
- B \(1.7\)
- C \(4\)
- D \(2.9\)
Answer & Solution
Correct Answer
(A) \(5.1\)
Step-by-step Solution
Detailed explanation
\(\frac{{dv}}{{dt}} = \phi - a\sqrt {2gh} = 0\) \((for\,maximum\,height)\) \(h = \frac{{{\phi ^2}}}{{2g{a^2}}} = \frac{{{{10}^{ - 8}}}}{{2 \times 9.8 \times {{10}^{ - 8}}}} = 5.1\,cm\)
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