There is a hole of area A at the bottom of cylindrical vessel..Water is filled up to a height h and water flows out in t second. If water is filled to a height of 4h,it will flow out in time equal to
Correct answer: C. 2t
- A. t
- B. 4t
- C. 2t
- D. t/4
Explanation
According to Torricelli's theorem, the velocity of efflux of a fluid under gravity through a small hole at the bottom of a container is given by v = √(2gh), where h is the height of the fluid column. The time taken to empty the container is inversely proportional to the velocity and directly proportional to the height of the fluid. Therefore, when the height is increased from h to 4h, the time taken becomes proportional to the square root of the height, t' = t√(4h)/√(h) = 2t. Hence, the time taken is doubled, making the correct answer 2t. The other options are incorrect as they do not accurately apply this principle.
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