A stone weights 250 N in air and 150 N in water. If the unit weight of water is 10000 N/m³, the volume of the stone is :
Try it first: pick an option, then read the explanation.
Asked in SSC JE 23.03.2021 (Evening Shift)
Detailed Explanation
According to Archimedes' principle, any body completely or partially submerged in a static fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the body.
1. Given data:
- Weight of stone in air \(W_{\text{air}} = 250\text{ N}\)
- Weight of stone in water \(W_{\text{water}} = 150\text{ N}\)
- Unit weight of water \(\gamma_w = 10,000\text{ N/m}^3\)
2. Calculate the buoyant force \(F_B\) (apparent loss in weight):
\[ F_B = W_{\text{air}} - W_{\text{water}} = 250\text{ N} - 150\text{ N} = 100\text{ N} \]
3. Apply Archimedes' principle for a completely submerged body:
\[ F_B = \gamma_w \times V_{\text{stone}} \]
4. Solve for the volume of the stone (\(V_{\text{stone}}\)):
\[ V_{\text{stone}} = \frac{F_B}{\gamma_w} = \frac{100\text{ N}}{10,000\text{ N/m}^3} = 0.01\text{ m}^3 \]
Why “0.01 m³” Is Correct
The buoyant upward thrust generated by the displaced water reduces the measured weight of the stone from \(250\text{ N}\) to \(150\text{ N}\), an exact loss of \(100\text{ N}\). Dividing this displaced water weight by the water's unit weight of \(10,000\text{ N/m}^3\) yields \(0.01\text{ m}^3\).
Why the Other Options Are Wrong
- A. 0.015 m³: 0.015 m³ results from incorrectly dividing 150 N by 10,000 N/m³ (using weight in water instead of loss of weight).
- B. 0.02 m³: 0.02 m³ results from arbitrary rounding or dividing 200 N by 10,000 N/m³.
- D. 0.025 m³: 0.025 m³ results from dividing the total air weight (250 N) by 10,000 N/m³.
Key Point
Loss of weight in water = Buoyant force F_B = γ_water · V_displaced.
Key Concepts for Students
- Archimedes' principle applies to bodies of any shape, whether fully submerged or floating.
- The buoyant force acts vertically upward through the centroid of the displaced fluid volume (centre of buoyancy).
- Specific gravity of the stone is W_air / (W_air − W_water) = 250 / 100 = 2.5.
Practice more: this is question 9 in Hydrostatic Pressure MCQs – Part 1. Try the whole set and check every answer instantly.