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Q113 (CDS-I/2012) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

A liquid is kept in a regular cylindrical vessel up to a certain height. If this vessel is replaced by another cylindrical vessel having half the area of cross- section of the bottom, the pressure on the bottom will—

Result
Your answer: —  ·  Correct: C
Explanation

The hydrostatic pressure at the bottom of a cylindrical vessel is determined by the formula P = ρgh, where ρ is the liquid density, g is gravitational acceleration, and h is the height of the liquid column. Crucially, hydrostatic pressure depends only on the height of the liquid column and is independent of the cross-sectional area of the vessel. In this scenario, a liquid is transferred from one vessel to another with half the cross-sectional area (A/2). Since the volume of the liquid (V = A × h) remains constant, reducing the area by half (A/2) forces the height to double (2h) to maintain the same volume. Because the pressure is directly proportional to the height (h), doubling the height results in the pressure at the bottom being increased to twice the earlier pressure.

Sources

  1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 6: Pressure, Winds, Storms, and Cyclones > Activity 6.1: Let us try and find out > p. 84
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