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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 4h, it will flow out in time equal to

Correct answer: C. 2t

  • A. t
  • B. 4t
  • C. 2t
  • D. t/4

Explanation

When the height of water in the cylindrical vessel is increased from 'h' to '4h', the pressure at the bottom increases proportionally. According to Torricelli's law, the velocity of efflux (flow) is directly proportional to the square root of the height of the liquid. Therefore, when the height is quadrupled, the velocity (and hence the time taken to flow out) is halved. Option C, 2t, is the correct choice as it correctly reflects this relationship. The other options incorrectly assume linear relationships between height and time taken to flow out.

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