Define relative density
Scenario
Aapko koi naya chemical milta hai aur aapko judge karna hai ki ye paani par tairega ya nahi.
Kya koi ek simple number hai jo bina unit ke humein bata de ki object paani se halka hai ya bhari?
Mental model
Water is the Gold Standard: Relative density bas ek comparison (ratio) hai object aur paani ke beech.
Hum paani (water) ko standard maan lete hain jiska mark `1` hota hai. Agar koi object paani se bhari (dense) hai, to uska relative density `1` se bada hoga aur wo doob jayega. Agar halka hai to `1` se chota hoga aur tair jayega.
Explanation
Normal density ka unit `kg/m³` hota hai aur iski numbers bahut badi aati hain (jaise Iron ki `7800 kg/m³`). Iss calculation ko simple banane ke liye science mein Relative Density ka use hota hai.
Relative density ek ratio hai. Hamesha object ki density ko water ki density se divide karke relative density nikali jati hai. (Formula: `Relative Density = Density of substance / Density of water`). Water ki density normally `1000 kg/m³` (ya `1 g/cm³`) mani jati hai.
Kyunki yeh do same quantities (density / density) ka division hai, dono units aapas mein cancel ho jate hain. Isliye Relative Density ki koi unit nahi hoti. Yeh sirf ek number (pure ratio) hota hai.
Fayda kya hai? Agar silver ki relative density `10.8` di gayi hai, to iska directly matlab hai ki silver paani se `10.8` guna zyada dense hai. Bina kisi unit conversion ke hum samajh sakte hain ki silver paani mein doob jayega.
Worked example
Problem: The relative density of silver is `10.8`. The density of water is `10^3 kg/m^3`. What is the density of silver in SI units?
- Relative density ka formula ratio ka hai.
- Silver ki density nikalne ke liye hum relative density ko water ki density se multiply karenge.
- Calculate karke answer aayega SI unit me.
Answer: `10800 kg/m^3`
Problem: Substance A has a relative density of `0.7`. Will it float or sink in water?
- Relative density `1` hone ka matlab hota ki paani ke barabar hai. `1` se kam hona matlab paani se halka hai.
Answer: It will float in water.
Key points
- No Units: Relative density is a pure ratio and therefore has no unit.
- Compared to Water: It is always calculated relative to the density of water (Density of substance / Density of water).
Common mistakes
- Attaching a unit to relative density: Students relative density ke aage `kg/m³` laga dete hain, jabki wo ek pure ratio hai jiska unit cancel out ho chuka hai.
Recall questions
- What is the SI unit of relative density?
- What is relative density?
- Does relative density have a unit?
Questions & answers
The volume of `50 g` of a substance is `20 cm^3`. If the density of water is `1 g/cm^3`, will the substance float or sink?
The substance will sink.
Approach: `Density of substance = Mass/Volume = 50 / 20 = 2.5 g/cm^3`. Since `2.5 > 1`, it will sink.
The relative density of silver is `10.8`. The density of water is `10³ kg/m³`. What is the density of silver in SI unit?
`10.8 × 10³ kg/m³`
Approach: Density = Relative density × Density of water.
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