AP EAMCET · PHYSICS · Mechanical Properties of Fluids
A large tank filled with water to a height ' \(h\) ' is to be emptied through a small hole at the bottom. The ratio of the time taken for the level to fall from ' \(h\) ' to \(\frac{'}{2}\) ' and that taken for the level to fall from \(\frac{1 h}{2}\) to ' 0 ' is
- A \(\sqrt{2}-1\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\sqrt{2}\)
- D \(\frac{1}{\sqrt{2}-1}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{2}-1\)
Step-by-step Solution
Detailed explanation
The time to emply the tank, \(\begin{aligned} & t=\sqrt{\frac{2 h}{g}} \Rightarrow t \propto \sqrt{h} \\ & \therefore \frac{t_1}{t_2} \\ &=\frac{\sqrt{h}-\sqrt{\frac{h}{2}}}{\sqrt{\frac{h}{2}}-\sqrt{0}}=(\sqrt{2}-1) \end{aligned}\)
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