GATE ME 2016 Set 2 — Question 51
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumForces on Submerged BodiesFluid Properties & StaticsFluid Mechanics
Fluid Mechanics → Fluid Properties & Statics → Forces on Submerged Bodies
Last updated
Question
Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius . The tank is filled with a liquid of density up to the tip of the plug. The gravitational acceleration is . Neglect the effect of the atmospheric pressure.
The force required to hold the plug in its position is
Correct answer
(A) 2ρ R² gL (1 - (π)/(4))
Solution
The force required to hold the plug is equal to the net vertical hydrostatic force acting on the semi-cylindrical surface.
The vertical force on a curved surface is equal to the weight of the liquid (real or imaginary) supported by the curved surface up to the free surface.
In this case, the volume of liquid above the curved surface is the volume of a rectangular block of dimensions minus the volume of the semi-cylinder.
Volume of rectangular block,
Volume of semi-cylinder,
Net volume of liquid above the surface,
The vertical force is the weight of this volume of liquid:Therefore, option (A) is correct.
The vertical force on a curved surface is equal to the weight of the liquid (real or imaginary) supported by the curved surface up to the free surface.
In this case, the volume of liquid above the curved surface is the volume of a rectangular block of dimensions minus the volume of the semi-cylinder.
Volume of rectangular block,
Volume of semi-cylinder,
Net volume of liquid above the surface,
The vertical force is the weight of this volume of liquid:Therefore, option (A) is correct.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Fluid Properties & Statics
2026 Set 1 Q24A steady incompressible laminar flow passes through a tube bend placed on a horizontal…2026 Set 1 Q25An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady…2026 Set 1 Q26Bernoulli’s equation CANNOT be applied between2026 Set 1 Q29A hydraulic crane supports a mass of with its piston-cylinder actuator, inclined at…2026 Set 1 Q53Water with a density of comes out of an industrial condenser through a…