Density Kaise Nikalein?
Mass naapna aa gaya, volume naapna bhi aa gaya. Ab dono ko jod kar kisi bhi cheez ki density nikaalenge, aur Dadi ki payal ka raaz bhi kholenge! 🧮✨
🧭 Is Post Mein
📖 Kahani: Dadi ki Payal Asli Chandi ki Hai?
Sunday ki dopahar thi. Rohan ki Dadi ne purane sandook se ek chhoti si payal nikaali aur boli, “Yeh meri Nani ne di thi. Sunaar kehta hai shayad poori chandi ki nahi hai. Kaise pata karein?”
Golu bola, “Chamak toh chandi jaisi hai, Dadi!” Priya hansi, “Chamak se kya hota hai? Steel bhi chamakta hai. Hum toh pichle post mein mass aur volume naapna seekh chuke hain. Chandi ki apni ek density hoti hai. Agar payal ki density usse milti hai, toh shayad asli hai!”
Teeno ne school wala chhota digital taraazu aur measuring cylinder nikaala. Taraazu par payal ka mass aaya 63 g. Cylinder mein 40 mL paani tha, payal dubaane par level 46 mL ho gaya.
Ab Golu ne pencil uthayi: “Volume = 46 − 40 = 6 cm³. Density = 63 ÷ 6 = …” Sab saans rok kar intezaar karne lage. 😮
Jawaab kya aaya, aur usse kya pata chalta hai? Aaj ka post isi hisaab ko step-by-step sikhayega. Kahani ka ant Examples mein milega! 🔍
🎯 Is Post Mein Kya Seekhenge
- Density nikaalne ke 4 aasaan steps: mass naapo, volume naapo, units check karo, bhaag do
- Formula ko ulta-seedha karna: Mass = Density × Volume aur Volume = Mass ÷ Density
- Thos (solid) ki density: seedhe aakaar wali aur tedhi-medhi dono ki
- Liquid (jaise tel, doodh) ki density kaise nikaalte hain
- Units badalna: g/cm³ ↔ kg/m³ (1 g/cm³ = 1000 kg/m³)
- Density se padarth ki pehchaan aur shuddhta (purity) ka andaaza
- Chhota tukda ho ya bada, ek hi padarth ki density same kyun rehti hai
🧱 Basics: Pehle Yeh Aana Chahiye
1. Density: kisi padarth ke ek unit volume (jaise 1 cm³) mein kitna mass bhara hai. Formula: Density = Mass ÷ Volume.
2. Mass naapna: balance (taraazu) se, g ya kg mein. Bartan ho toh Tare dabao ya uska mass ghatao.
3. Volume naapna: liquid ka measuring cylinder se; seedhi cheez ka l × b × h se; tedhi cheez ka displacement se (V₂ − V₁). Yaad rakho 1 mL = 1 cm³.
4. Bhaag aur decimal: 46 ÷ 50 = 0.92 jaise jawaab aate hain. Decimal se ghabraana nahi hai.
💡 Concept: Density Nikaalne ka Pakka Tareeka
Step 1: Sawaal samjho. Density batati hai ki padarth kitna “thasa-thas bhara” hai. 1 cm³ lohe mein lagbhag 7.9 g mass hota hai, jabki 1 cm³ paani mein sirf 1 g. Isliye lohe ki density paani se lagbhag 8 guna hai.
🪜 Density nikaalne ke 4 steps
- Step A: Mass naapo (balance se). Jaise payal = 63 g.
- Step B: Volume naapo (cylinder, l × b × h, ya V₂ − V₁). Jaise payal = 6 cm³.
- Step C: Units check karo. Mass g mein aur volume cm³ (ya mL) mein ho toh jawaab g/cm³ mein aayega. Mass kg mein aur volume m³ mein ho toh kg/m³ mein.
- Step D: Bhaag do. Density = Mass ÷ Volume = 63 ÷ 6 = 10.5 g/cm³. Jawaab ke saath unit zaroor likho!
Kyun bhaag dete hain? Kyunki hume “1 cm³ ke hisse mein kitna mass aaya” chahiye. 63 g ko 6 barabar cm³ mein baanto, toh har cm³ ke hisse 10.5 g aata hai. Yeh bilkul “ek kilo ka daam” nikaalne jaisa hai.
🔄 Formula ko ulta-seedha karna
Step 2: Ek formula se teen kaam ho sakte hain:
- Density = Mass ÷ Volume (density chahiye)
- Mass = Density × Volume (mass chahiye). Jaise 10 cm³ lohe ka mass = 7.9 × 10 = 79 g.
- Volume = Mass ÷ Density (volume chahiye). Jaise 280 g shahad (density 1.4 g/cm³) ka volume = 280 ÷ 1.4 = 200 cm³.
Yaad rakhne ki chaal: neeche diye “Density Triangle” mein jo cheez chahiye, use ungli se dhak do. Jo bacha, wahi formula hai!
🪨 Thos (solid) ki density
Step 3: Seedhe aakaar wali cheez (jaise aluminium ka gutka): scale se l, b, h naapo, volume = l × b × h. Balance se mass naapo. Phir bhaag do. Jaise 5 cm × 4 cm × 2 cm = 40 cm³, mass 108 g, density = 108 ÷ 40 = 2.7 g/cm³.
Step 4: Tedhi-medhi cheez (jaise pathar, payal): mass balance se, volume displacement se (V₂ − V₁). Golu ka pathar: 30 g aur 12 cm³, toh density = 30 ÷ 12 = 2.5 g/cm³.
🧴 Liquid ki density
Step 5: Liquid ko bina bartan ke tol nahi sakte. Isliye:
- Khaali measuring cylinder ko tolo: jaise 60 g.
- Usme tel daalo, jaise 50 mL tak (meniscus ka neeche wala hissa, aankh seedh mein).
- Ab bhare cylinder ko tolo: jaise 106 g.
- Tel ka mass = 106 − 60 = 46 g. Density = 46 ÷ 50 = 0.92 g/mL.
Kyun ghatana zaroori hai? 106 g mein cylinder ka kaanch bhi shaamil hai. Hume sirf tel ka mass chahiye. (Digital balance par khaali cylinder rakh kar Tare daba do, toh ghatana bhi nahi padega.)
📏 Units badalna
Step 6: Density ki SI unit kg/m³ hai, par lab mein g/cm³ ya g/mL zyada aasaan hai. Rishta: 1 g/cm³ = 1000 kg/m³. Toh g/cm³ se kg/m³ banane ke liye × 1000, aur ulta karne ke liye ÷ 1000. Jaise paani: 1 g/cm³ = 1000 kg/m³; aluminium: 2.7 g/cm³ = 2700 kg/m³.
Ek line mein: mass naapo, volume naapo, units milao, bhaag do, aur unit ke saath jawaab likho. Phir us density ko paani (1 g/cm³) se ya kisi jaani-maani table se milao! 🎯
🖼️ Diagrams: Picture se Samjho
🔐 Deep Concept: Density ke Gehre Raaz
1. 1 g/cm³ = 1000 kg/m³ kyun? 1 g = 1/1000 kg, aur 1 m = 100 cm, toh 1 m³ = 100 × 100 × 100 = 10,00,000 cm³. Isliye 1 cm³ = 1/10,00,000 m³. Ab 1 g/cm³ = (1/1000 kg) ÷ (1/10,00,000 m³) = 10,00,000 ÷ 1000 = 1000 kg/m³.
2. Density padarth ki “pehchaan” hai: shuddh chandi ki density lagbhag 10.5 g/cm³, sone ki 19.3, aluminium ki 2.7. Ek hi taapmaan par yeh number padarth ke saath badalta nahi, chahe tukda chhota ho ya bada. Isliye anjaan dhaatu ki density naap kar table se milaane par andaaza lagta hai ki woh kya ho sakti hai.
3. Purani kahani: kehte hain ki yunaan (Greece) ke vaigyanik Archimedes se raja ne poocha tha ki mukut mein milawat hai ya nahi. Mukut ko todna nahi tha. Archimedes ne paani hataane wale tareeke se mukut ka volume naapne ka vichaar kiya: agar mukut ka volume utne hi mass ke shuddh sone se zyada hai, toh usme koi halki dhaatu mili hai. Yahi density wala tark hai!
4. Ausat (average) density: khokhli cheez (jaise steel ki katori ya jahaaz) mein andar hawa bhi hoti hai. Tab hum kul mass ÷ kul bahari volume lete hain, jise ausat density kehte hain. Steel 7.9 g/cm³ ka hai, par katori ki ausat density 1 se kam ho jaaye toh woh tairti hai.
5. Sateek naap ka mahatva: payal jaisi chhoti cheez ka volume sirf 6 cm³ hai. Agar cylinder 1 mL tak hi naapta hai aur reading mein 1 mL ki galti ho jaaye, toh density 63 ÷ 7 = 9 ya 63 ÷ 5 = 12.6 bhi aa sakti hai! Isliye chhoti cheezon ke liye patla cylinder lo, reading 2–3 baar lo, aur zaroorat ho toh kai ek jaisi cheezein saath mein naapo.
6. Agle post ka trailer: density taapmaan aur dabaav (pressure) se thodi badal sakti hai. Garam karne par zyadatar cheezein phailti hain, toh density ghat jaati hai. Iske baare mein Post 8 mein vistaar se padhenge.
✏️ Examples: Hisaab Lagao
⚖️ Difference Table: Kis Cheez ki Density Kaise Nikaalein?
| Cheez | Mass kaise | Volume kaise | Density |
|---|---|---|---|
| Seedhe aakaar ka solid (gutka, eent) | Balance par seedha | l × b × h | Mass ÷ (l × b × h) |
| Tedha-medha solid (pathar, payal) | Balance par seedha | Displacement: V₂ − V₁ | Mass ÷ (V₂ − V₁) |
| Liquid (tel, doodh) | (Bhara cylinder) − (khaali cylinder), ya Tare | Cylinder ki reading | Liquid ka mass ÷ reading |
| Bahut chhoti cheezein (kanche, daane) | Kai ek saath tolo | Kai ek saath dubao | Kul mass ÷ kul volume |
Units ki chhoti table:
| Mass ki unit | Volume ki unit | Density ki unit | Badalna |
|---|---|---|---|
| g | cm³ ya mL | g/cm³ ya g/mL | × 1000 → kg/m³ |
| kg | m³ | kg/m³ (SI unit) | ÷ 1000 → g/cm³ |
🚫 Misconceptions: Log aisa sochte hain… lekin
❌ Galat: “Lohe ki badi rod ki density chhoti keel se zyada hogi.”
✅ Sach: rod ka mass zyada hai, par volume bhi utna hi zyada hai. Density (mass ÷ volume) dono ki barabar, lagbhag 7.9 g/cm³.
❌ Galat: “Density = Volume ÷ Mass.”
✅ Sach: Density = Mass ÷ Volume. Mass upar, volume neeche. Ulta karoge toh ek bilkul alag (aur galat) number aayega.
❌ Galat: “Bhare cylinder ka mass hi liquid ka mass hai.”
✅ Sach: usme cylinder ka mass bhi shaamil hai. Khaali cylinder ka mass ghatao (ya Tare karo).
❌ Galat: “1 g/cm³ aur 1 kg/m³ ek hi baat hai.”
✅ Sach: 1 g/cm³ = 1000 kg/m³. Paani ki density 1 g/cm³ ya 1000 kg/m³ hai, 1 kg/m³ nahi.
❌ Galat: “Jawaab mein sirf number likhna kaafi hai, jaise 2.7.”
✅ Sach: bina unit ke jawaab adhoora hai. 2.7 g/cm³ aur 2.7 kg/m³ mein 1000 guna farq hai!
❌ Galat: “Density match ho gayi toh 100% pakka asli hai.”
✅ Sach: density ek achha sanket hai. Do alag milawaton ka jod bhi kabhi wahi density de sakta hai, aur naap mein galti bhi ho sakti hai. Pakki jaanch ke liye aur tests bhi hote hain.
🔤 Key Terms (Exam mein English shabd hi likhna)
❓ FAQs
1. Density nikaalne ke liye kya-kya naapna padta hai?
Sirf do cheezein: mass (balance se) aur volume (cylinder, l × b × h ya displacement se). Phir Density = Mass ÷ Volume.
2. g/cm³ aur g/mL mein kya farq hai?
Koi farq nahi, kyunki 1 mL = 1 cm³. Liquid ke liye aksar g/mL aur solid ke liye g/cm³ likhte hain.
3. g/cm³ ko kg/m³ mein kaise badlein?
1000 se guna karo. Jaise 0.8 g/cm³ = 800 kg/m³. Ulta karne ke liye 1000 se bhaag do.
4. Kya ek hi padarth ke alag size ke tukdon ki density alag hoti hai?
Nahi. Ek hi taapmaan aur dabaav par density padarth ka gun hai, size ya shape ka nahi.
5. Agar density aur volume pata ho toh mass kaise nikaalein?
Mass = Density × Volume. Jaise 0.92 g/mL ke 100 mL tel ka mass = 92 g.
6. Density se milawat kaise pakdi ja sakti hai?
Har shuddh padarth ki ek tay density hoti hai. Agar naapi gayi density usse kaafi alag aaye, toh shayad usme kuch mila hai. Jaise doodh mein paani milane se density thodi ghat jaati hai, jise lactometer pakad leta hai.
🧪 Activity: Pathar aur Paani ki Density Nikaalo
Saamaan: digital balance, 100 mL ka measuring cylinder, paani, dhaaga, ek chhota pathar (jo cylinder mein aa jaaye), copy-pencil. (Ho sake toh ek gutka ya rubber bhi.)
Part A: Pathar ki density
Part B: Paani ki density
Kya dikhega: pathar ki density aksar 2.5 se 3 g/cm³ ke aas-paas aayegi (paani se zyada, isliye pathar doobta hai). Paani ki density lagbhag 1 g/mL aayegi. Thoda sa farq (jaise 0.98 ya 1.02) naap ki chhoti galtiyon se aata hai, ghabraana nahi.
Nishkarsh: kisi bhi cheez ki density nikaalne ke liye bas uska mass aur volume sahi-sahi naapo aur bhaag do. Jis cheez ki density paani se zyada, woh paani mein doobti hai.
🤔 Socho: Part A mein agar pathar ke neeche hawa ka ek bulbula phans jaaye, toh nikli hui density zyada aayegi ya kam?
Kam. Bulbula bhi jagah gherta hai, toh V₂ zyada aayega aur volume asli se bada naapa jaayega. Mass wahi rahega, par bada number se bhaag dene par density chhoti aayegi. Isliye pathar ko halka sa hila kar bulbula nikaal do, phir reading lo.
Yeh activity NCERT ki Class 8 Science book Curiosity (Chapter 9) ke density nikaalne wale hisse par aadharit hai, aur yahan apne shabdon mein samjhayi gayi hai.
🏠 Mini Experiments (Ghar pe)
Kya seekha? Tel ki density paani se kam aayegi (lagbhag 0.9), doodh ki thodi zyada (lagbhag 1.03). Rasoi scale 1 g tak hi naapta hai, isliye jawaab “lagbhag” hi aayega.
Ek seedhi, aayataakar sabun ki tikki ki lambai, chaudai, oonchai scale se cm mein naapo aur volume nikaalo. Rasoi scale par uska mass naapo. Density nikaalo. Ab andaaza lagao: yeh paani mein doobegi ya tairegi? Phir ek baalti mein daal kar check karo! (Kai sabun doobte hain, kuch khaas sabun jinme hawa bhari hoti hai, tairte hain.)
Ek aaloo ke ek bade aur ek chhote tukde ki density displacement se nikaalo (mass scale par, volume nishaan wale jug/botal mein). Dono ki density lagbhag barabar aayegi, kyunki padarth ek hi hai. Isse “size se density nahi badalti” khud dekh loge.
🧠 Think Like a Scientist
Sawaal: Rohan kehta hai, “Badi cheez ki density zyada hoti hai.” Priya kehti hai, “Nahi, density size par nirbhar nahi.” Kaun sahi hai?
Scientist ka tareeka dekho
1. Observe (dekho): lohe ki bhaari rod paani mein doobti hai, aur chhoti keel bhi doobti hai.
2. Guess (anumaan): agar Rohan sahi hai, toh rod ki density keel se zyada aani chahiye. Agar Priya sahi hai, toh dono ki barabar.
3. Test (jaanch): dono ka mass balance se aur volume displacement se naapo. Keel: 15.8 g, 2 cm³. Rod: 395 g, 50 cm³.
4. Result (nateeja): keel ki density = 15.8 ÷ 2 = 7.9 g/cm³; rod ki = 395 ÷ 50 = 7.9 g/cm³. Bilkul barabar!
5. Conclusion (nishkarsh): Priya sahi hai. Bada tukda hone se mass aur volume dono ek hi anupaat mein badhte hain, toh density wahi rehti hai. Density padarth ka gun hai, size ka nahi.
🌍 Real Life Mein Density ka Hisaab
- 🥛 Doodh ki jaanch: dairy mein lactometer naam ka yantra doodh ki density se pata lagata hai ki usme paani mila hai ya nahi.
- ⛽ Petrol pump: grahak petrol ki density test maang sakte hain. Petrol ki density ek tay range (lagbhag 720–775 kg/m³) mein honi chahiye; usse bahut alag ho toh milawat ka shak hota hai.
- 💍 Sunaar: gehnon ki shuddhta jaanchne ke kai tareekon mein density wala tark bhi kaam aata hai.
- 🚢 Jahaaz aur naav: engineer hisaab lagate hain ki samaan bharne ke baad bhi jahaaz ki ausat density paani se kam rahe, taaki woh tairta rahe.
- 🏗️ Imaarat: engineer saamaan ki density aur volume se uska kul mass (Mass = Density × Volume) nikaal kar tay karte hain ki chhat ya pul kitna bojh sahega.
- 🍯 Rasoi: 1 kg shahad ki botal, 1 kg tel ki botal se chhoti hoti hai. Kyun? Shahad ki density zyada hai, toh utne mass ke liye kam volume chahiye!
🔁 Recap: Poora Post Ek Nazar Mein
- Density = Mass ÷ Volume; isse Mass = Density × Volume aur Volume = Mass ÷ Density bhi nikalte hain.
- 4 steps: mass naapo → volume naapo → units check karo → bhaag do (aur unit likho).
- Regular solid: volume = l × b × h. Irregular solid: volume = V₂ − V₁.
- Liquid: (bhara cylinder − khaali cylinder) ÷ reading. Bartan ka mass ghatana zaroori.
- 1 g/cm³ = 1000 kg/m³; SI unit kg/m³. g/cm³ = g/mL.
- Ek hi padarth ke chhote-bade tukdon ki density barabar hoti hai.
- Density se padarth ki pehchaan aur milawat ka andaaza lagta hai (lactometer, petrol ki jaanch).
- Paani se kam density = tairna, zyada density = doobna.
✍️ Fill in the Blanks
- Density = ______ ÷ Volume.
- Mass = Density × ______.
- 1 g/cm³ = ______ kg/m³.
- Liquid ka mass nikaalne ke liye bhare cylinder ke mass mein se ______ cylinder ka mass ghatate hain.
- Ek hi padarth ke chhote aur bade tukde ki density ______ hoti hai.
- 2700 kg/m³ = ______ g/cm³.
Answers
1) Mass · 2) Volume · 3) 1000 · 4) khaali · 5) barabar (same) · 6) 2.7
✅ True / False
- 50 g mass aur 25 cm³ volume wali cheez ki density 2 g/cm³ hai.
- Lohe ki badi rod ki density chhoti keel se zyada hoti hai.
- 0.8 g/cm³ density wale 100 cm³ liquid ka mass 80 g hai.
- Density nikaalne ke liye volume ko mass se bhaag dete hain.
- 920 kg/m³ = 9.2 g/cm³.
- Density naap kar kisi dhaatu ki shuddhta ka andaaza lagaya ja sakta hai.
Answers (kyun ke saath)
1) True: 50 ÷ 25 = 2 g/cm³.
2) False: mass aur volume dono ek hi anupaat mein badhte hain, density wahi (lagbhag 7.9 g/cm³) rehti hai.
3) True: Mass = 0.8 × 100 = 80 g.
4) False: mass ko volume se bhaag dete hain (Mass ÷ Volume).
5) False: 920 ÷ 1000 = 0.92 g/cm³.
6) True: shuddh padarth ki density tay hoti hai; bahut alag density milawat ka sanket hai (par yeh akela pakka saboot nahi).
🔘 MCQs
Q1. Ek cheez ka mass 80 g aur volume 40 cm³ hai. Uski density? (a) 0.5 g/cm³ (b) 2 g/cm³ (c) 120 g/cm³ (d) 3200 g/cm³
✅ (b) 2 g/cm³: 80 ÷ 40 = 2.
(a) 0.5 = 40 ÷ 80; formula ulta lagaya.
(c) 120 = 80 + 40; jodna galat hai.
(d) 3200 = 80 × 40; guna karna galat hai.
Q2. Shahad ki density 1.4 g/cm³ hai. 50 cm³ shahad ka mass kitna? (a) 35.7 g (b) 51.4 g (c) 70 g (d) 48.6 g
✅ (c) 70 g: Mass = Density × Volume = 1.4 × 50 = 70 g.
(a) 35.7 = 50 ÷ 1.4; yahan bhaag nahi, guna karna tha.
(b) 51.4 = 50 + 1.4; jodna galat.
(d) 48.6 = 50 − 1.4; ghatana galat.
Q3. 2.7 g/cm³ ko kg/m³ mein likho. (a) 27 (b) 270 (c) 2700 (d) 0.0027
✅ (c) 2700 kg/m³: g/cm³ ko kg/m³ banane ke liye × 1000; 2.7 × 1000 = 2700.
(a) sirf × 10 kiya.
(b) sirf × 100 kiya.
(d) ÷ 1000 kar diya, ulta.
Q4. Khaali cylinder 60 g ka hai. 100 mL liquid daalne par mass 140 g ho jaata hai. Liquid ki density? (a) 1.4 g/mL (b) 0.8 g/mL (c) 0.6 g/mL (d) 80 g/mL
✅ (b) 0.8 g/mL: liquid ka mass = 140 − 60 = 80 g; density = 80 ÷ 100 = 0.8.
(a) 1.4 = 140 ÷ 100; cylinder ka mass ghatana bhool gaye.
(c) 0.6 = 60 ÷ 100; yeh toh cylinder ka mass hai.
(d) 80 sirf mass hai, volume se bhaag nahi diya.
Q5. Ek gutka 4 cm × 3 cm × 2 cm ka hai aur mass 192 g hai. Density? (a) 8 g/cm³ (b) 21.3 g/cm³ (c) 0.125 g/cm³ (d) 4608 g/cm³
✅ (a) 8 g/cm³: volume = 4 × 3 × 2 = 24 cm³; 192 ÷ 24 = 8.
(b) 21.3 = 192 ÷ 9; lambaiyon ko joda (4 + 3 + 2), guna karna tha.
(c) 0.125 = 24 ÷ 192; formula ulta.
(d) 4608 = 192 × 24; guna karna galat.
Q6. In mein se kaunsi cheez paani mein tairegi? Density: (a) 2.5 g/cm³ (b) 7.9 g/cm³ (c) 0.6 g/cm³ (d) 1.4 g/cm³
✅ (c) 0.6 g/cm³: paani (1 g/cm³) se kam density wali cheez tairti hai.
(a) 2.5 (jaise kaanch) paani se zyada, doobega.
(b) 7.9 (loha) doobega.
(d) 1.4 bhi 1 se zyada hai, doobega.
Q7. Kisi dhaatu ka 10 cm³ ka tukda 27 g ka hai. Usi dhaatu ke 30 cm³ ke tukde ka mass? (a) 27 g (b) 81 g (c) 9 g (d) 54 g
✅ (b) 81 g: density = 27 ÷ 10 = 2.7 g/cm³ (same dhaatu, same density); mass = 2.7 × 30 = 81 g.
(a) 27 g toh chhote tukde ka hai; volume 3 guna hua toh mass bhi 3 guna.
(c) 9 = 27 ÷ 3; ulta kiya.
(d) 54 = 27 × 2; volume 2 guna nahi, 3 guna hua hai.
Q8. Lohe ki density 7.9 g/cm³ hai. 158 g lohe ka volume kitna hoga? (a) 20 cm³ (b) 1248.2 cm³ (c) 150.1 cm³ (d) 165.9 cm³
✅ (a) 20 cm³: Volume = Mass ÷ Density = 158 ÷ 7.9 = 20.
(b) 1248.2 = 158 × 7.9; guna galat.
(c) 150.1 = 158 − 7.9; ghatana galat.
(d) 165.9 = 158 + 7.9; jodna galat.
🔗 Assertion–Reason
Options: (a) A aur R dono sahi, aur R, A ko samjhata hai · (b) A aur R dono sahi, par R, A ko nahi samjhata · (c) A sahi, R galat · (d) A galat, R sahi
1. A: Lohe ki chhoti keel aur badi rod ki density barabar hoti hai. R: Density padarth ka gun hai, uske size par nirbhar nahi karti.
✅ (a): dono sahi, aur R hi A ka kaaran hai: padarth same hai, toh density same.
2. A: Liquid ki density nikaalte waqt khaali cylinder ka mass ghatana zaroori hai. R: Measuring cylinder par mL ke nishaan bane hote hain.
✅ (b): dono baatein sahi hain, par nishaan hona ghatane ka kaaran nahi. Asli kaaran: bhare cylinder ke mass mein cylinder ka mass bhi juda hota hai.
3. A: 1 g/cm³ = 1 kg/m³. R: 1 kg = 1000 g.
✅ (d): A galat hai, kyunki 1 g/cm³ = 1000 kg/m³. R sahi hai.
📝 Very Short Answer (1 mark)
1. Density ka formula likho.
Density = Mass ÷ Volume.
2. Density ki SI unit kya hai?
kg/m³ (kilogram per cubic metre).
3. Density aur volume pata ho toh mass kaise nikaalenge?
Mass = Density × Volume.
4. 1 g/cm³ kitne kg/m³ ke barabar hai?
1000 kg/m³.
5. Doodh ki density jaanchne wale yantra ka naam batao.
Lactometer.
📝 Short Answer (2–3 marks)
1. Ek tedhe-medhe pathar ki density nikaalne ke steps likho.
(i) Balance se pathar ka mass naapo. (ii) Measuring cylinder mein paani lo aur V₁ padho. (iii) Pathar ko dhaage se poora dubao aur V₂ padho. (iv) Volume = V₂ − V₁. (v) Density = Mass ÷ (V₂ − V₁), unit g/cm³.
2. Kisi liquid ki density kaise nikaaloge? Ek udaharan do.
Khaali cylinder tolo (jaise 60 g), usme tay volume liquid daalo (jaise 50 mL) aur dobara tolo (jaise 106 g). Liquid ka mass = 106 − 60 = 46 g. Density = 46 ÷ 50 = 0.92 g/mL.
3. Lohe ke bade aur chhote tukde ki density barabar kyun hoti hai?
Bada tukda hone par mass aur volume dono ek hi anupaat mein badhte hain. Isliye unka bhaag (Mass ÷ Volume) wahi rehta hai. Jaise 15.8 g/2 cm³ = 7.9 aur 395 g/50 cm³ = 7.9 g/cm³.
4. 0.8 g/cm³ ko kg/m³ mein badlo aur tareeka samjhao.
1 g/cm³ = 1000 kg/m³ (kyunki 1 g = 1/1000 kg aur 1 cm³ = 1/10,00,000 m³). Toh 0.8 g/cm³ = 0.8 × 1000 = 800 kg/m³.
📝 Long Answer (5 marks)
1. Ek regular solid (gutka), ek irregular solid (pathar) aur ek liquid (tel) ki density nikaalne ke tareeke udaharan sahit samjhao.
Gutka: scale se l, b, h naapo; volume = l × b × h (jaise 5 × 4 × 2 = 40 cm³). Balance se mass (108 g). Density = 108 ÷ 40 = 2.7 g/cm³.
Pathar: mass balance se (30 g). Displacement se volume: V₁ = 50 mL, V₂ = 62 mL, volume = 12 cm³. Density = 30 ÷ 12 = 2.5 g/cm³.
Tel: khaali cylinder 60 g; 50 mL tel ke saath 106 g; tel ka mass 46 g. Density = 46 ÷ 50 = 0.92 g/mL.
Dhyaan rakho: balance 0 se shuru ho, aankh meniscus ki seedh mein ho, cheez poori dooba ho, bulbule na hon, aur jawaab unit ke saath likho. Gutka aur pathar paani (1 g/cm³) se ghane hain, isliye doobenge; tel halka hai, isliye paani par tairega.
2. Density ki madad se kisi gehne ki shuddhta ka andaaza kaise lagaya ja sakta hai? Payal ke udaharan se samjhao aur is tareeke ki seemaayein (limits) bhi batao.
Har shuddh padarth ki ek tay density hoti hai; shuddh chandi ki lagbhag 10.5 g/cm³. Payal ka mass balance se naapo (63 g) aur volume displacement se (46 − 40 = 6 cm³). Density = 63 ÷ 6 = 10.5 g/cm³, jo chandi se milti hai, toh payal shayad shuddh chandi ki hai. Agar density 8 g/cm³ aati (48 g ÷ 6 cm³), toh usme koi halki dhaatu mili hai.
Seemaayein: (i) chhoti cheez ka volume bahut kam hota hai, toh 1 mL ki galti se bhi density bahut badal jaati hai; (ii) do alag dhaatuon ka mishran bhi kabhi milti-julti density de sakta hai; (iii) gehne mein khokhla hissa ya phansi hawa ho toh volume galat aata hai. Isliye density ek achha sanket hai, pakki jaanch ke liye aur tests chahiye.
📰 Case-Based Question
Meena ne rasoi ke scale par ek katori rakh kar Tare dabaya. Phir usne baari-baari se 100 mL paani, 100 mL sarson ka tel aur 100 mL shahad daal kar tola (har baar katori saaf karke). Mass aaye: paani 100 g, tel 92 g, shahad 140 g. Meena ne socha, “Agar teeno ko ek hi glass mein dheere-dheere daaloon, toh kaun upar rahega?”
Q1. Teeno ki density nikaalo.
Paani = 100 ÷ 100 = 1 g/mL; tel = 92 ÷ 100 = 0.92 g/mL; shahad = 140 ÷ 100 = 1.4 g/mL.
Q2. Glass mein upar se neeche tak kaunsi parat (layer) kaunsi hogi?
Sabse kam density wala upar: tel (upar) → paani (beech) → shahad (neeche). (Shahad dheere-dheere paani mein ghulta bhi hai, isliye parat thodi der hi saaf dikhegi.)
Q3. 250 mL shahad ka mass kitna hoga?
Mass = 1.4 × 250 = 350 g.
Q4. 46 g tel ka volume kitna hoga?
Volume = 46 ÷ 0.92 = 50 mL.
🚀 HOTS
1. Do ek jaise dikhne wale cube hain, dono ka volume 10 cm³ hai. Ek ka mass 27 g aur doosre ka 79 g hai. Kaunsa aluminium ka (2.7 g/cm³) aur kaunsa lohe ka (7.9 g/cm³) hai?
Pehle ki density = 27 ÷ 10 = 2.7 g/cm³ → aluminium. Doosre ki = 79 ÷ 10 = 7.9 g/cm³ → loha. Bina kaate-pheeke, sirf tol kar pehchaan ho gayi!
2. Shuddh doodh ki density lagbhag 1.03 g/mL hoti hai. Ek sample ki density 1.01 g/mL aayi. Kya andaaza lagaoge?
Paani ki density (1.00) doodh se kam hai. Doodh mein paani milaane par mishran ki density 1.03 se ghat kar 1.00 ki taraf jaati hai. 1.01 aana batata hai ki shayad paani mila hai. (Pakki jaanch ke liye aur tests bhi kiye jaate hain, kyunki doodh ki malai jaisi cheezein bhi density badalti hain.)
3. Steel ki density 7.9 g/cm³ hai, phir bhi ek khokhli steel ki band gend paani mein tairti hai. Gend ka mass 400 g aur bahari volume 500 cm³ hai. Samjhao.
Gend ki ausat density = kul mass ÷ kul bahari volume = 400 ÷ 500 = 0.8 g/cm³, jo paani (1) se kam hai, isliye gend tairti hai. Andar bhari hawa volume to badhati hai par mass bahut kam jodti hai.
🏆 Olympiad Corner
1. 100 g paani mein 25 g namak ghola gaya. Ghol ka volume 110 mL maapa gaya. Ghol ki density batao (2 decimal tak).
Ghol ka kul mass = 100 + 25 = 125 g. Density = 125 ÷ 110 = 1.136… ≈ 1.14 g/mL. Dhyaan do: namak ghulne par volume 100 + namak ke volume jitna nahi badhta, isliye volume naapna padta hai.
2. Ek sone ki angoothi ka mass 9.65 g hai (sona: 19.3 g/cm³). Agar woh shuddh hai toh uska volume kitna hoga? Kya 1 mL ke khaanon wale cylinder se ise sahi naap sakte hain?
Volume = 9.65 ÷ 19.3 = 0.5 cm³. Yeh ek khaane (1 mL) se bhi kam hai! Is cylinder se sahi naap mushkil hai; bahut patla, baareek nishaanon wala cylinder ya doosre sateek tareeke chahiye.
3. Ek tanki ka volume 2 m³ hai aur usme mitti ka tel (800 kg/m³) bhara hai. Tel ka mass kitna hai? Ise grams per cm³ mein bhi likho.
Mass = 800 × 2 = 1600 kg. Density 800 kg/m³ = 800 ÷ 1000 = 0.8 g/cm³.
Har option pe tap karo, turant pata chalega sahi ya galat.
Q1. Ek metal piece: mass 135 gram, volume 50 cm³. Density?
(a) 0.37 gram/cm³
❌ Galat: Volume ÷ mass kiya: 50 ÷ 135 ≈ 0.37. Sahi: 135 ÷ 50 = 2.7.
(b) 2.7 gram/cm³
✅ Sahi! Density = mass ÷ volume = 135 ÷ 50 = 2.7 gram/cm³.
(c) 6750 gram/cm³
❌ Galat: Mass × volume kiya: 135 × 50 = 6750. Density = 135 ÷ 50 = 2.7.
(d) 185 gram/cm³
❌ Galat: Mass + volume kiya: 135 + 50 = 185. Density = 135 ÷ 50 = 2.7.
Q2. Oil ki density 0.9 gram/cm³ hai. 300 cm³ oil ka mass?
(a) 333.3 gram
❌ Galat: Volume ÷ density kiya: 300 ÷ 0.9 ≈ 333.3. Mass ke liye multiply: 0.9 × 300 = 270.
(b) 300 gram
❌ Galat: Volume ko hi mass maana (300). Oil ki density 0.9: 0.9 × 300 = 270.
(c) 270 gram
✅ Sahi! Mass = density × volume = 0.9 × 300 = 270 gram.
(d) 299.1 gram
❌ Galat: Density subtract kar di: 300 − 0.9 = 299.1. Sahi: 0.9 × 300 = 270.
Q3. Iron ki density 7.9 gram/cm³ hai. 237 gram iron ka volume?
(a) 1872.3 cm³
❌ Galat: Multiply kar diya: 237 × 7.9 = 1872.3. Volume = 237 ÷ 7.9 = 30.
(b) 0.033 cm³
❌ Galat: Divide reverse kiya: 7.9 ÷ 237 ≈ 0.033. Sahi: 237 ÷ 7.9 = 30.
(c) 229.1 cm³
❌ Galat: Subtract kar diya: 237 − 7.9 = 229.1. Volume = 237 ÷ 7.9 = 30.
(d) 30 cm³
✅ Sahi! Volume = mass ÷ density = 237 ÷ 7.9 = 30 cm³.
Q4. Empty measuring cylinder 80 gram ka hai. 50 mL liquid daalne pe total 150 gram. Liquid ki density?
(a) 1.4 gram/cm³
✅ Sahi! Liquid ka mass = 150 − 80 = 70 gram. Density = 70 ÷ 50 = 1.4 gram/cm³.
(b) 3 gram/cm³
❌ Galat: Cylinder ka mass subtract nahi kiya: 150 ÷ 50 = 3. Pehle 150 − 80 = 70, phir 70 ÷ 50 = 1.4.
(c) 1.6 gram/cm³
❌ Galat: Empty cylinder ka mass le liya: 80 ÷ 50 = 1.6. Liquid = 150 − 80 = 70; 70 ÷ 50 = 1.4.
(d) 0.71 gram/cm³
❌ Galat: Volume ÷ mass kiya: 50 ÷ 70 ≈ 0.71. Density = 70 ÷ 50 = 1.4.
Q5. Ek metal ka 5 cm³ ka piece 40 gram ka hai. Usi metal ka 20 cm³ ka piece kitne gram ka hoga?
(a) 40 gram
❌ Galat: Mass same maan liya (40). Bada piece, zyada mass: 8 × 20 = 160.
(b) 160 gram
✅ Sahi! Density = 40 ÷ 5 = 8 gram/cm³ (same metal, same density). Mass = 8 × 20 = 160 gram.
(c) 10 gram
❌ Galat: Ratio reverse lagaya: 40 × 5 ÷ 20 = 10. Sahi: (40 ÷ 5) × 20 = 160.
(d) 55 gram
❌ Galat: Volume ka difference mass mein add kiya: 40 + 15 = 55. Sahi: 8 × 20 = 160.
📚 Aur Padho (External Reference)
- NCERT Class 8 Science Curiosity, Chapter 9 (official PDF)
- DIKSHA: Sarkar ka free learning platform, NCERT ke videos ke liye
💖 CharuMam Motivation
Aaj Dadi ki payal ne humein sikhaya ki chamak se asliyat pata nahi chalti. Asli pehchaan andar ki “density” se hoti hai: kitna thos, kitna bharpoor.
Beta, insaan ke saath bhi aisa hi hai. Bahar ki chamak, naye kapde ya dikhaawa thodi der ka hai. Tumhari asli density hai tumhari mehnat, imaandaari aur seekhne ki lagan. Roz thoda-thoda padho, sawaal poochho, galti se seekho. Tumhara “andar ka mass” badhta jaayega, aur duniya ki koi bhi jaanch tumhe asli hi paayegi! 💪✨
— CharuMam
▶️ Is topic ki video dekhein: Density of Common Materials
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