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A body weighs 50 grams in air and 40 grams in water. How much would it weigh in a liquid of specific gravity 1.5?
1. 30 grams
2. 35 grams
3. 65 grams
4. 45 grams

1 Answer

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Correct Answer - Option 2 : 35 grams

CONCEPT:

  • The specific gravity of a substance is the ratio of the density of a substance to the density of water or any other reference substance.

\( specific \ gravity= \frac{ρ_{Given substance}}{ρ _{Reference Substance}}\)

  • Archimedes's principle states that "upward buoyant force exerted by a fluid on a body which is immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction "

CALCULATION:

Given- Equivalent weight in water = mg =  40g, Actual weight = mg = 50 g, ρwater  = 1 g/cm3, and Specific gravity of liquid (ρliquid) = 1.5

  • The upward thrust acting on the object is given by

⇒ Actual weight -  Buoyant force = Equivalent weight in water

⇒ 50g - ρwaterVg = 40g

⇒ ρwaterVg = 10 g

⇒ V =10 Cm3

  • The weight of the body in a liquid of specific gravity 1.5 is

⇒ Actual weight  - Buoyant force  = weight in liquid

⇒ 50  - ρliquidVg =  50 - 1.5  × 10 = 35g

  • Hence, option 2 is the answer

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