Density, specific gravity — Hinglish notes

2.2.2 · Physics › Fluid Mechanics

Density KYA hai?

Yeh definition kyun? Mass akela nahi batata ki matter kitna "concentrated" hai — ek tonne air aur ek tonne lead dono ka mass same hai, lekin size bilkul alag hai. Volume se divide karne par "size" ka effect hat jaata hai aur material ki ek intrinsic property milti hai.

Conversion scratch se kaise nikaalte hain: Start karo $1 g = 1 0^{- 3} kg$ se aur $1 cm = 1 0^{- 2} m$ se, to $1 cm^{3} = (1 0^{- 2})^{3} = 1 0^{- 6} m^{3}$ . Phir $\frac{1 0 ^{- 3}}{1 0 ^{- 6}} = 1 0^{3}$ . Koi magic factor yaad nahi karna — tum khud bana sakte ho.

Specific gravity (relative density) KYA hai?

Ratio kyun? Kyunki yeh turant bata deta hai "kya yeh paani mein float karega?" aur bina units liye materials compare karne deta hai. SG > 1 → doobta hai, SG < 1 → tairata hai (paani mein).

4 °C par paani kyun? Paani 4 °C par sabse dense hota hai ( $\approx 1000 kg/m^{3}$ exactly), jo ek clean, reproducible standard deta hai.

Derivation: ek mixture ki density

Maano tum masses ko volumes ke saath mix karo jo simply add ho jaate hain (koi chemical shrinking nahi).

Step 1 — Total mass: $m = m_{1} + m_{2}$ . Kyun? Mass conserved rahta hai jab cheezein combine karte ho. Step 2 — Total volume: $V = V_{1} + V_{2}$ . Kyun? Assume karo volumes add hote hain (ideal mixing). Step 3 — Definition apply karo: $ρ_{mix} = \frac{m _{1} + m _{2}}{V _{1} + V _{2}}$

Worked Examples

Common mistake Classic errors ko steel-man karna

(a) "Bhaari cheezein hamesha dense hoti hain." Kyun sahi lagta hai: heavy ↔ density dono "weight" se related lagte hain. Fix: ek bhaari log phir bhi tair sakta hai — jo matter karta hai woh hai mass per volume, akela mass nahi. 1000 kg ka ek air balloon ek 1 g ke sand grain se kam dense hai.

(b) Mix karte waqt densities ko directly average karna. Kyun sahi lagta hai: averaging natural lagti hai. Fix: Tum sirf equal volumes ke liye average kar sakte ho. Equal masses ke liye harmonic mean $\frac{2 ρ _{1} ρ _{2}}{ρ _{1} + ρ _{2}}$ use karna hoga, kyunki dense substance kam volume occupy karta hai.

(c) SG ko units dena. Kyun sahi lagta hai: density mein units hain, to uske ratio mein bhi "hone chahiye." The fix: Yeh $\frac{kg/m ^{3}}{kg/m ^{3}}$ hai → units cancel ho jaate hain. SG ek pure number hai.

(d) Unit conversion mein $1 0^{3}$ bhool jaana. Hamesha rebuild karo $1 g/cm^{3} = 1000 kg/m^{3}$ .

Recall Feynman: ek 12-saal ke bacche ko explain karo

Density hai "andar ka stuff kitna crowded hai." Bahut log ek chhoti lift mein bhar do = crowded = dense. Wahi log ek football field mein phela do = crowded nahi = dense nahi. Specific gravity bas ek score-card hai jo compare karta hai ki koi cheez paani ke comparison mein kitni crowded hai. Score 1 se upar = doobta hai, 1 se neeche = tairata hai. Easy!

Active Recall — answers cover kar lo

Density kya hai (words aur formula mein)?

Mass per unit volume,

ρ = m / V

, SI unit kg/m³.

Density ka SI unit kya hai?

kilogram per cubic metre,

kg/m^{3}

1 g/cm^{3}

ko kg/m³ mein convert karo.

1000 kg/m^{3}

(

1 0^{3}

ka factor).

Specific gravity define karo.

Kisi substance ki density ka paani ki density (

1000 kg/m^{3}

) se ratio; dimensionless.

SG < 1 wala object paani mein kyun tairata hai?

Uski density paani se kam hai, isliye buoyant force weight ke barabar ho sakta hai jab partly submerged ho.

ρ_{1}, ρ_{2}

ke EQUAL MASSES mix karne par density?

Harmonic mean:

\frac{2 ρ _{1} ρ _{2}}{ρ _{1} + ρ _{2}}

ρ_{1}, ρ_{2}

ke EQUAL VOLUMES mix karne par density?

Arithmetic mean:

\frac{ρ _{1} + ρ _{2}}{2}

Paani ki density dono unit systems mein?

1 g/cm^{3} = 1000 kg/m^{3}

Agar gold ka SG 19.3 hai, to uski density kg/m³ mein kya hai?

19.3 \times 1000 = 19300 kg/m^{3}

Akela mass "matter kitna packed hai" ka bura measure kyun hai?

Yeh size ko ignore karta hai; intrinsic property paane ke liye volume se divide karna zaroori hai.

Connections

Pressure in fluids — pressure $P = ρ g h$ directly density par depend karta hai.
Buoyancy and Archimedes' principle — float/sink, density (SG) comparison se decide hota hai.
Relative density measurement (hydrometer) — instrument jo SG directly read karta hai.
Continuity equation — incompressible flow ke liye, $ρ$ constant rahta hai.
Pascal's law