GATE AG 2008 • Q40 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Ideal and real fluids, properties of fluids

Question Statement:

The weight of a hollow sphere is 100 N. If it floats in water just fully submerged, the external diameter of the sphere is

Options:

  • (A) 112 mm
  • (B) 213 mm
  • (C) 269 mm
  • (D) 315 mm

Official Answer Key:

C

Step-by-Step Solution & Explanation

Just-submerged floating ⇒ buoyant force = weight: ρwater·g·V = 100 N → V = 100/(1000×9.81) = 0.01019 m³. V=(4/3)πr³ → r = (3V/4π)^(1/3) = 0.1345 m → D = 269.0 mm.

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