Density, specific gravity: Question bank — Hinglish deep dive

2.2.2 · D5 · Physics › Fluid Mechanics › Density, specific gravity

Recall karo do tools jo hum throughout use karte hain:

Density $ρ = m / V$ — mass packed per unit of space (dekho Density, specific gravity).
Specific gravity $SG = ρ_{substance} / ρ_{water}$ , ek pure number jisme $ρ_{water} = 1000 kg/m^{3}$ .

True or false — justify karo

Recall Verdict

aur reason dono zaroori hain Ek bhaari object hamesha ek halke object se zyada dense hoti hai. ::: False. Density hai mass per volume; ek bada halka log ek pebble se zyada weight rakhta hai phir bhi float karta hai kyunki uska mass kaafi zyada space pe spread hai. Ek iron cube ka size double karne se uski density double ho jaati hai. ::: False. Mass aur volume dono $8 \times$ badhte hain (side cubed), isliye unka ratio $ρ = m / V$ unchanged rehta hai — density material ki intrinsic property hai. Specific gravity ke units density jaisi hoti hain. ::: False. Ye ek ratio hai $\frac{kg/m ^{3}}{kg/m ^{3}}$ , isliye units cancel ho jaate hain aur SG ek pure dimensionless number hai. Agar SG $= 1$ exactly ho, toh object poori tarah submerged hoke float karta hai jisme uska top surface ke level pe hota hai. ::: True. Equal densities matlab weight aur maximum buoyancy 100% submersion pe balance karte hain, isliye ye kisi bhi depth pe neutrally hang karta hai — na upar jaata hai na neecha. Dekho Buoyancy and Archimedes' principle. Seawater ka ek cup pure water ke ek cup se zyada dense hota hai. ::: True. Dissolved salt lagbhag same volume mein mass add karta hai, isliye $ρ$ badhti hai (lagbhag $1025 kg/m^{3}$ ) — isliye samundar mein float karna aasaan hota hai. Ek block ko aadha kaat dene se uski specific gravity aadhi ho jaati hai. ::: False. SG material pe depend karta hai, quantity pe nahi; har aadhe ka same $ρ$ hoga aur isliye same SG hoga. Water at $4^{\circ} C$ ko reference isliye use kiya jaata hai kyunki ye sabse thanda temperature hai jo water ho sakta hai. ::: False. Water isse thanda ho sakta hai ( $0^{\circ} C$ tak freeze hone se pehle); $4^{\circ} C$ isliye choose kiya jaata hai kyunki water wahan sabse dense hota hai, jo ek clean, reproducible standard deta hai. Gold ka SG ( $19.3$ ) uski density $g/cm^{3}$ mein ke barabar hai. ::: True. Kyunki water $1 g/cm^{3}$ hai, kisi bhi density ko $g/cm^{3}$ mein $1$ se divide karne par number unchanged rehta hai — ye numerical coincidence hi wajah hai ki dono match karte hain.

Spot the error

Recall Flawed step dhundo, phir fix batao

" $ρ_{1}$ aur $ρ_{2}$ ke equal volumes mix karte hue, maine densities average ki: $\frac{ρ _{1} + ρ _{2}}{2}$ ." ::: Yahan sahi hai — equal volumes ke liye arithmetic mean sahi hai, kyunki equal $V$ har density ko total mass mein equally contribute karwata hai. Trap ye hai ki isse equal masses ke liye copy kar lo. " $ρ_{1}$ aur $ρ_{2}$ ke equal masses mix karte hue, maine densities average ki." ::: Error. Equal masses ke liye denser liquid kam volume leta hai, isliye tumhe harmonic mean $\frac{2 ρ _{1} ρ _{2}}{ρ _{1} + ρ _{2}}$ use karna chahiye; plain average denser wale ko over-count karta hai. "Oil ka SG $= 0.8$ hai, isliye uski density $0.8 kg/m^{3}$ hai." ::: Error. SG ek ratio hai; water se multiply karo: $ρ = 0.8 \times 1000 = 800 kg/m^{3}$ . $\times 1000$ bhool jaana classic galti hai. " $1 g/cm^{3} = 1 kg/m^{3}$ kyunki maine sirf units swap ki." ::: Error. Grams to kg $\times 1 0^{- 3}$ hai lekin $cm^{3}$ to $m^{3}$ $\times 1 0^{- 6}$ hai; net factor $1 0^{3}$ hai, isliye ye $1000 kg/m^{3}$ hai. "Ice paani mein sink karti hai kyunki ice ek solid hai aur solids liquids se zyada dense hote hain." ::: Error. Solids usually apne liquid se zyada dense hote hain, lekin water ek rare exception hai — ice ( $917 kg/m^{3}$ ) liquid water se kam dense hai, isliye ye float karti hai. "Kyunki pressure $P = ρ g h$ hai, deep water shallow water se zyada dense hai." ::: Error. $P = ρ g h$ model mein water ko incompressible treat kiya jaata hai, isliye $ρ$ constant rehta hai; pressure badhti hai kyunki $h$ badhta hai, $ρ$ nahi. Dekho Pressure in fluids.

Why questions

Recall Mechanism explain karo, sirf label nahi

Hum mass ko volume se kyun divide karte hain, subtract kyun nahi karte? ::: Hum jaanna chahte hain "kitna concentrated" — ek rate of mass per unit space. Division jawab deta hai "ek unit volume mein kitna"; subtraction incompatible quantities mix kar deta aur total size pe depend karta. Specific gravity turant float-or-sink kyun bata deta hai, jabki raw density kg/m³ mein ek glance mein nahi? ::: SG pehle se water ke against measure hai, isliye threshold simply $1$ hai: upar sink, neeche float. Raw density ke liye tumhe pehle water $= 1000$ yaad karna padta aur compare karna padta. Density ko intrinsic property kyun kehte hain jabki mass aur volume nahi? ::: Mass aur volume is baat ke saath scale karte hain ki tum kitna material lete ho, lekin unka ratio fixed conditions pe ek given material ke liye fixed hota hai — ye substance ko fingerprint karta hai. Mixing formula mein "volumes add" assume kyun karna zaroori hai? ::: Kuch mixtures shrink ho jaate hain (water + alcohol tighter pack hote hain), isliye $V \neq = V_{1} + V_{2}$ ; simple formula tabhi hold karta hai jab aisi koi contraction na ho. Hydrometer denser liquid mein zyada upar kyun float karta hai? ::: Ek denser liquid har unit submerged volume ke liye zyada buoyant force supply karta hai, isliye hydrometer ka kam hissa sink karna padta hai apna weight balance karne ke liye, aur ye zyada upar ride karta hai — zyada bada SG read karta hai. Dekho Relative density measurement (hydrometer). Ek hi density ke do objects ke mass bilkul alag kyun ho sakte hain? ::: Density sirf mass-to-volume ratio fix karti hai; same material ke ek bade aur ek chote tukde ka shared $ρ$ hoga lekin alag amounts of material honge, isliye alag masses.

Edge cases

Recall Boundary aur degenerate scenarios

Perfect vacuum ki "density" kya hai, aur kya formula survive karta hai? ::: Volume mein koi mass nahi, $m = 0$ , isliye $ρ = 0/ V = 0$ . Formula theek hai jab tak $V \neq = 0$ . Kya $ρ = m / V$ zero volume ke liye evaluate ho sakta hai? ::: Nahi — $V = 0$ se divide karna undefined hai, jo physical fact se match karta hai ki "no space" mein concentration ki baat nahi ho sakti. Do liquids jo mix nahi hote (oil on water) — kya pair ke liye ek single density hoti hai? ::: Ek uniform density nahi; har layer apna $ρ$ rakhti hai. "Mixture density" tabhi sense karta hai jab unhe ek uniform body mein blend karo. Agar tum ek gas ko half volume mein compress karo (mass unchanged), density ka kya hoga? ::: Ye double ho jaati hai, kyunki $ρ = m / V$ aur $V$ aadha hua — gases isliye hain ki Continuity equation aur $P = ρ g h$ ki "incompressible" assumption liquids ke liye reserved hai. Equal masses ka harmonic mean jab $ρ_{1} = ρ_{2} = ρ$ : kya milta hai? ::: $\frac{2 ρ \cdot ρ}{ρ + ρ} = ρ$ — jab ingredients identical hon toh dono mean formulas same value pe aa jaate hain, ek achha sanity check hai. Ek block jiska SG exactly $0$ ho (imaginary massless block) paani pe rakho — wo kahan baithega? ::: Ye poori tarah surface pe baith jaata hai zero submersion ke saath, kyunki $V_{sub} / V = SG = 0$ ; zero weight support karne ke liye koi buoyancy ki zaroorat nahi. Kya ek solid ko heat karne se uski density change hoti hai, aur kaunsi direction mein? ::: Usually density kam hoti hai: heat volume expand karta hai jabki mass fixed rehta hai, isliye $ρ = m / V$ drop karta hai. (Water $0$ aur $4^{\circ} C$ ke beech famous exception hai.)

Connections

Buoyancy and Archimedes' principle — yahan har float/sink verdict isi pe based hai.
Pressure in fluids — $P = ρ g h$ mein $ρ$ isliye hai ki "deep = denser" ek trap hai.
Relative density measurement (hydrometer) — hydrometer question ke peeche SG-reading instrument.
Continuity equation — incompressibility $ρ$ ko constant rakhti hai.
Pascal's law