An odd shaped body weighing 7.5 kg and occupying 0.01 cubic meter volume will be completely submerged in a fluid having specific gravity of ...............
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2 MARCH 2017 Morning Shift
Detailed Explanation
For a body to be completely submerged in neutral equilibrium (neither sinking to the bottom nor floating to break the free surface), its average density must equal the density of the surrounding fluid.
1. Calculate the mass density of the body:
\[ \rho_{\text{body}} = \frac{\text{Mass}}{\text{Volume}} = \frac{7.5\text{ kg}}{0.01\text{ m}^3} = 750\text{ kg/m}^3 \]
2. Condition for complete submergence in neutral equilibrium:
A body remains completely submerged when the upward buoyant force equals its downward weight:
\[ F_B = W \;\implies\; \rho_{\text{fluid}} g V = \rho_{\text{body}} g V \;\implies\; \rho_{\text{fluid}} = \rho_{\text{body}} = 750\text{ kg/m}^3 \]
3. Calculate the required specific gravity (\(S\)) of the fluid:
\[ S = \frac{\rho_{\text{fluid}}}{\rho_{\text{water}}} = \frac{750\text{ kg/m}^3}{1000\text{ kg/m}^3} = 0.75 \]
Why “0.75” Is Correct
Because the body has a mass density of \(750\text{ kg/m}^3\), placing it in a liquid with specific gravity \(0.75\) produces a buoyant force exactly equal to its weight when fully immersed.
Why the Other Options Are Wrong
- A. 1: In water (S = 1.0, ρ = 1000 kg/m³), the body is lighter than water and floats with 25% of its volume above surface.
- B. 1.2: In a fluid with S = 1.2 (ρ = 1200 kg/m³), the body floats with more than a third of its volume above surface.
- C. 0.8: In a fluid with S = 0.8 (ρ = 800 kg/m³), the body still floats with a small fraction above surface.
Key Point
Neutral buoyancy condition: ρ_body = ρ_fluid ⇒ S_fluid = ρ_body / 1000.
Key Concepts for Students
- If ρ_body < ρ_fluid, the body floats partially submerged.
- If ρ_body = ρ_fluid, the body remains suspended in neutral equilibrium anywhere within the fluid.
- If ρ_body > ρ_fluid, the body sinks to the bottom.
Practice more: this is question 16 in Hydrostatic Pressure MCQs – Part 2. Try the whole set and check every answer instantly.