JEE Mains · Physics · STD 11 - 9.1 fluid mechanics
A cylindrical vessel of cross-section \(A\) contains water to a height \(h\) . There is a hole in the bottom of radius \('a'\) . The time in which it will be emptied is
- A \(\frac{{2A}}{{\pi {a^2}}}\sqrt {\frac{h}{g}} \)
- B \(\frac{{\sqrt 2A }}{{\pi {a^2}}}\sqrt {\frac{h}{g}} \)
- C \(\frac{{2\sqrt 2A }}{{\pi {a^2}}}\sqrt {\frac{h}{g}} \)
- D \(\frac{A}{{\sqrt 2 \pi {a^2}}}\sqrt {\frac{h}{g}} \)
Answer & Solution
Correct Answer
(B) \(\frac{{\sqrt 2A }}{{\pi {a^2}}}\sqrt {\frac{h}{g}} \)
Step-by-step Solution
Detailed explanation
Let the rate of falling water level be \( - \frac{{dh}}{{dt}}\) Initially at \(t = 0\,;\,h = h\) \(t = t\,;h = 0\) \(Then,\,A\left( { - \frac{{dh}}{{dt}}} \right) = \pi {a^2}.v\) \(\left[ {Velocity\,of\,efflux\,of\,liquid\,v = \sqrt {2gh} } \right]\) Integrating both sides…
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