Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 19 of 37
The speed of efflux of a liquid flowing through a small hole at the bottom of a large tank is measured to be \( 9.8 \text{ m/s} \). What is the height of the fluid surface above the hole? (Assume \( g = 9.8 \text{ m/s}^2 \))
A
\( 9.8 \text{ m} \)
B
\( 19.6 \text{ m} \)
C
\( 1.0 \text{ m} \)
D
\( 4.9 \text{ m} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( 4.9 \text{ m} \)
Concept:

Torricelli's Law equates the speed of efflux to the kinematics of free fall.

Formula:

$$ v = \sqrt{2gh} $$

Solution:

  • We are given \( v = 9.8 \text{ m/s} \) and \( g = 9.8 \text{ m/s}^2 \).
  • Square both sides of the equation: \( v^2 = 2gh \).
  • Isolate height \( h \): \( h = \frac{v^2}{2g} \).
  • Substitute values: \( h = \frac{(9.8)^2}{2 \times 9.8} \).
  • Cancel one 9.8 from numerator and denominator: \( h = \frac{9.8}{2} = 4.9 \text{ m} \).


Why other options are incorrect:

Failing to square the velocity or omitting the factor of 2 leads to incorrect answers like 9.8 or 19.6 m.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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