Mass aur Volume Kaise Napein?
Taraazu, measuring cylinder aur ek chhota sa pathar. Aaj seekhenge ki kisi bhi cheez ka mass aur volume sahi-sahi kaise naapte hain! ⚖️🧪
🧭 Is Post Mein
📖 Kahani: Nani ki Recipe aur “Ek Glass” ka Jhagda
Diwali se pehle Nani ne Priya, Golu aur Rohan ko besan ke laddoo banane ki zimmedari di. Recipe ki purani copy mein likha tha: “Besan 500 g, ghee 200 g, doodh 100 mL.”
Golu ne besan ka dabba uthaya aur bola, “500 g? Bas andaaz se do mutthi daal deta hoon!” Rohan ne doodh ke liye ek bada steel ka glass utha liya: “Ek glass doodh, ho gaya 100 mL.”
Priya ne turant roka: “Ruko! Andaaz se laddoo bigad jaayenge. Rasoi mein digital taraazu (weighing scale) hai aur doodh naapne wala nishaan wala jug bhi. Pehle sahi-sahi naapte hain.”
Taraazu par besan tola gaya, jug mein doodh 100 ke nishaan tak bhara gaya. Laddoo ekdum Nani jaise bane! 😋 Tabhi Golu ne aangan se ek tedha-medha pathar utha kar poocha: “Doodh ka volume toh jug se naap liya. Par is tedhe pathar ka volume kaise naapoge? Iske toh na seedhe kinaare hain, na koi nishaan!”
Sab soch mein pad gaye. 🤔 Pichle post mein humne seekha tha ki Density = Mass ÷ Volume. Par density nikaalne ke liye pehle mass aur volume dono sahi-sahi naapne aane chahiye. Aaj wahi seekhenge, aur Golu ke pathar ka jawaab bhi dhoondhenge! 🔍
🎯 Is Post Mein Kya Seekhenge
- Mass kaise naapte hain: taraazu (beam balance) aur digital weighing balance
- “Tare” ya zero button ka sahi istemaal, aur bartan ka mass ghatana
- Liquid ka volume: measuring cylinder se, aur meniscus ko sahi tareeke se padhna
- Ek chhote khaane ki value (least count) kaise nikaalte hain
- Seedhe aakaar wali (regular) cheez ka volume: lambai × chaudai × oonchai
- Tedhe-medhe (irregular) thos ka volume: paani hataane ka tareeka (displacement method)
- Units ka rishta: 1 kg = 1000 g, 1 L = 1000 mL, 1 mL = 1 cm³
🧱 Basics: Pehle Yeh Aana Chahiye
1. Mass: kisi cheez mein kitna padarth (matter) bhara hai. Units: milligram (mg), gram (g), kilogram (kg).
2. Volume: koi cheez kitni jagah gherti hai. Units: millilitre (mL), litre (L), cubic centimetre (cm³), cubic metre (m³).
3. Naapna (measurement) kya hai? Kisi cheez ko ek tay “unit” se milaana. Jaise “500 g” ka matlab hai: 1 gram jaisi 500 ikaiyon ke barabar mass.
4. Ghatana (subtraction): is post mein kai baar “baad wala reading − pehle wala reading” karna hoga. Jaise 62 − 50 = 12.
💡 Concept: Mass aur Volume Naapne ke Tareeke
Step 1: Andaaz kaafi kyun nahi? “Do mutthi” ya “ek glass” har insaan ke liye alag hota hai. Golu ki mutthi chhoti, Papa ki badi. Science mein (aur achhi rasoi mein bhi!) hume aisi tay units chahiye jo sabke liye ek jaisi hon: gram, kilogram, millilitre, litre.
⚖️ Part 1: Mass kaise naapein?
Step 2: Taraazu (beam balance). Sabzi wale bhaiya ka do palde wala taraazu yaad karo. Ek palde mein sabzi, doosre mein jaane-pehchaane mass ke baat (weights) jaise 500 g, 1 kg. Jab dandi bilkul seedhi (barabar) ho jaati hai, toh dono taraf ka mass barabar hota hai.
Kyun? Barabar dandi ka matlab hai dono palde ek jitni taakat se neeche kheeche ja rahe hain. Isliye sabzi ka mass = baaton ka kul mass.
Step 3: Digital weighing balance. Aaj kal dukaanon, rasoi aur school lab mein digital balance hota hai. Cheez rakho, screen par seedha number aa jaata hai, jaise 245 g. Lab wale balance 0.01 g tak bhi bata dete hain.
Step 4: “Tare” (ya Zero) button ka jaadu. Aata seedha palde par nahi rakh sakte, katori chahiye. Par katori ka bhi mass hota hai! Do tareeke hain:
- Tareeka A (Tare): khaali katori rakho → Tare dabao → screen 0 dikhayegi → ab aata daalo. Jo number aaye, woh sirf aate ka mass hai.
- Tareeka B (Ghatao): pehle khaali katori tolo (jaise 150 g), phir aata daal kar tolo (jaise 650 g). Aate ka mass = 650 − 150 = 500 g.
Step 5: Sahi tolne ke niyam. Balance ko samtal (flat) jagah par rakho, pehle 0 check karo, garam cheez seedhe mat rakho, aur tolte waqt haath ya hawa se mat hilao.
Step 6: Mass ki units ka rishta. 1 kg = 1000 g aur 1 g = 1000 mg. Dawai ki goli par “500 mg” likha ho toh woh 0.5 g hai.
🧪 Part 2: Liquid ka volume kaise naapein?
Step 7: Measuring cylinder. Yeh ek lamba, patla, paardarshi (transparent) bartan hota hai jis par mL ke nishaan bane hote hain. Liquid daalo aur nishaan padho. Rasoi ka nishaan wala jug bhi isi kaam aata hai, par patla cylinder zyada sahi naapta hai.
Step 8: Meniscus kya hai? Cylinder mein paani daal kar dhyaan se dekho: paani ki upari satah bilkul seedhi nahi hoti, beech mein thodi neeche dhansi hui (U jaisi) hoti hai. Is mudi hui satah ko meniscus kehte hain. Paani deewaron se thoda “chipak” kar upar chadh jaata hai, isliye kinaare upar aur beech neeche.
Step 9: Sahi reading ka niyam. Cylinder ko samtal mez par rakho, aankh ko meniscus ki seedh (eye level) mein laao, aur meniscus ke sabse neeche wale hisse ki reading lo. Upar se ya neeche se tirchi nazar se dekhoge toh reading galat aayegi. (Paara yaani mercury jaise liquid mein satah ulti, upar ko ubhri hoti hai; wahan sabse upar wala hissa padhte hain.)
Step 10: Ek chhote khaane ki value (least count). Har nishaan par number nahi likha hota. Do likhe hue numbers ke beech ka antar lo aur beech ke khaanon (divisions) ki ginti se bhaag do. Jaise 10 mL aur 20 mL ke beech 5 khaane hain, toh ek khaana = (20 − 10) ÷ 5 = 2 mL.
📦 Part 3: Thos (solid) ka volume kaise naapein?
Step 11: Seedhe aakaar wali cheez (regular solid). Ek dabba, eent ya rubber jaisi cheez jiske kinaare seedhe hon, uska volume = lambai × chaudai × oonchai. Agar sab cm mein hain, toh volume cm³ mein aayega. Jaise 5 cm × 4 cm × 3 cm wala dabba = 60 cm³.
Step 12: Tedhi-medhi cheez (irregular solid): Golu ka pathar! Iske liye paani hataane ka tareeka (displacement method) use karte hain:
- Measuring cylinder mein itna paani lo ki pathar poora doob sake. Reading likho: V₁ (jaise 50 mL).
- Pathar ko dhaage se baandh kar dheere se paani mein utaaro (girao mat, chheente udenge).
- Paani ka level upar chadh jaayega. Nayi reading likho: V₂ (jaise 62 mL).
- Pathar ka volume = V₂ − V₁ = 62 − 50 = 12 mL = 12 cm³.
Kyun? Do cheezein ek hi jagah ek saath nahi reh sakti. Pathar jitni jagah gherta hai, utna paani hat kar upar chala jaata hai. Isliye paani kitna upar chadha = pathar ka volume.
Step 13: Units ka rishta. 1 mL = 1 cm³, 1 L = 1000 mL = 1000 cm³, aur 1 m³ = 1000 L. Isliye cylinder par mL padh kar seedhe cm³ likh sakte ho.
Ek line mein: mass ke liye balance, liquid ke volume ke liye measuring cylinder (meniscus ka neeche wala hissa, aankh seedh mein), seedhi cheez ke liye l × b × h, aur tedhi cheez ke liye V₂ − V₁. In dono naapon se agle post mein density nikaalenge! 🎯
🖼️ Diagrams: Picture se Samjho
🔐 Deep Concept: Sahi Naap ke Raaz
1. Least count aur sateekta (accuracy): kisi yantra se jo sabse chhota hissa naapa ja sakta hai, use least count kehte hain. Rasoi ka scale aksar 1 g tak, lab ka balance 0.01 g tak naapta hai. 100 mL wale cylinder mein ek khaana aksar 1 mL ka hota hai. Jitna chhota least count, utni baareek naap.
2. Patla cylinder, beaker se behtar kyun? Patle cylinder mein thoda sa liquid daalne par bhi level kaafi upar chadhta hai, toh chhota antar bhi saaf dikhta hai. Chaude beaker mein level bahut kam hilta hai, isliye beaker ke nishaan sirf “lagbhag” naap batate hain.
3. Overflow can (Eureka can): agar pathar cylinder mein na samaaye toh ek aisa bartan lo jiski side mein nali (spout) ho. Usme nali tak paani bharo. Ab pathar daalo: jitna paani nali se bahar girega, use measuring cylinder mein ikattha karke naap lo. Woh pathar ka volume hai.
4. Tairne wali cheez (jaise cork) ka volume: cork doobta nahi, toh seedha displacement nahi chalega. Tareeka: ek bhaari “sinker” (jaise lohe ka nut) dhaage se baandho. Pehle sirf sinker ko doobao, reading lo (V₁). Phir sinker ke saath cork ko bhi poora doobao, reading lo (V₂). Cork ka volume = V₂ − V₁.
5. Galtiyan jo naap bigaadti hain: cylinder mein hawa ke bulbule, chheente udna, paani sokhne wali cheez (chalk, sponge) ka volume naapna, ya cheez ka poora na doobna. In sab se volume galat aata hai.
6. Mass aur wazan (weight) mein farq: roz ki bhaasha mein hum “wazan 500 g” bolte hain, par science mein gram aur kilogram mass ki units hain. Weight woh khinchaav (force) hai jo Prithvi kisi cheez par lagati hai. Chaand par tumhara mass wahi rahega, par weight lagbhag 1/6 reh jaayega. (Force ke baare mein aage ki kakshaon mein vistaar se padhoge.)
✏️ Examples: Naapo aur Nikaalo
⚖️ Difference Table: Kya Naapna Hai, Kaise Naapein?
| Kya naapna hai | Yantra / Tareeka | Unit | Dhyaan rakho |
|---|---|---|---|
| Mass (thos ya liquid) | Beam balance ya digital balance | g, kg, mg | Pehle 0 check karo; bartan ke liye Tare ya ghatao |
| Liquid ka volume | Measuring cylinder (ya nishaan wala jug) | mL, L | Aankh seedh mein, meniscus ka neeche wala hissa |
| Regular solid ka volume | Scale se naapo: l × b × h | cm³, m³ | Teeno lambaiyan ek hi unit mein |
| Irregular solid ka volume | Displacement: V₂ − V₁ (ya overflow can) | mL = cm³ | Cheez poori dooba ho, bulbule na hon |
| Tairne wali cheez ka volume | Sinker ke saath displacement | cm³ | Sinker ka volume alag se ghatao |
🚫 Misconceptions: Log aisa sochte hain… lekin
❌ Galat: “Meniscus ke kinaare (upar wali line) ki reading lete hain.”
✅ Sach: paani jaise liquid ke liye meniscus ka sabse neeche wala hissa padhte hain, aur aankh uski seedh mein rakhte hain.
❌ Galat: “mL aur cm³ alag-alag cheezein hain, inme badalna mushkil hai.”
✅ Sach: 1 mL = 1 cm³, bilkul barabar. 20 mL paani 20 cm³ jagah gherta hai.
❌ Galat: “Pathar daalne ke baad jo reading aayi (62 mL), wahi pathar ka volume hai.”
✅ Sach: pathar ka volume sirf badhottari hai: 62 − 50 = 12 mL.
❌ Galat: “Jo cheez badi dikhti hai, uska mass bhi zyada hoga.”
✅ Sach: bada thermocol ka dabba ek chhote lohe ke nut se halka ho sakta hai. Mass ko taraazu se hi naapo, aankhon se nahi.
❌ Galat: “Katori mein rakh kar tola toh jo number aaya woh aate ka mass hai.”
✅ Sach: usme katori ka mass bhi juda hai. Tare dabao ya katori ka mass ghatao.
❌ Galat: “Mass aur weight ek hi cheez hain.”
✅ Sach: mass padarth ki maatra hai (kg); weight ek khinchaav (force) hai. Roz ki bhaasha mein dono mil jaate hain, par science mein farq hai.
🔤 Key Terms (Exam mein English shabd hi likhna)
❓ FAQs
1. Mass naapne ke liye kaunsa yantra use hota hai?
Balance: do palde wala beam balance (taraazu) ya digital weighing balance.
2. Meniscus kya hota hai aur ise kaise padhte hain?
Cylinder mein liquid ki mudi hui upari satah ko meniscus kehte hain. Paani ke liye aankh seedh mein rakh kar uska sabse neeche wala hissa padhte hain.
3. Kya 1 mL aur 1 cm³ barabar hain?
Haan, bilkul. Isliye measuring cylinder ki mL wali reading ko seedhe cm³ mein likh sakte hain.
4. Pathar ya chaabi ka volume kaise nikaalein?
Displacement method se: cylinder mein paani ki reading V₁ lo, cheez dooba kar V₂ lo. Volume = V₂ − V₁.
5. Tare button kya karta hai?
Bartan rakhne ke baad Tare dabane se screen 0 ho jaati hai. Ab jo daaloge, sirf uska mass dikhega.
6. Chheeni (sugar) ya namak ka volume displacement se kyun nahi naap sakte?
Kyunki yeh paani mein ghul jaate hain (Post 1 yaad karo!). Ghulne wali cheez ke liye paani ki jagah koi aisa liquid chahiye jisme woh na ghule, ya doosra tareeka.
🧪 Activity: Ek Pathar ka Mass aur Volume Naapo
Saamaan: ek digital ya beam balance, 100 mL ka measuring cylinder (na ho toh nishaan wala jug), paani, dhaaga, aur kuch chhoti cheezein jo paani mein doobti hain aur ghulti nahi: ek pathar, lohe ki chaabi, kancha, rubber (eraser), aur ek chhota steel ka nut.
Kya dikhega: har cheez dubaane par paani ka level upar chadhega. Badi cheez ke liye zyada, chhoti ke liye kam. Rubber ke liye dono tareekon se lagbhag ek jaisa volume aayega, jo sabit karta hai ki displacement tareeka sahi kaam karta hai.
Nishkarsh: mass balance se, aur volume measuring cylinder se (displacement dwara) naapa ja sakta hai. Inhi dono naapon se agle post mein har cheez ki density nikaalenge.
🤔 Socho: agar pathar ke neeche ek hawa ka bulbula phans jaaye, toh naapa gaya volume zyada aayega ya kam?
Zyada. Bulbula bhi jagah gherta hai, toh paani pathar aur bulbule dono ke barabar upar chadhega. 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 mass aur volume naapne wale hisse par aadharit hai, aur yahan apne shabdon mein samjhayi gayi hai.
🏠 Mini Experiments (Ghar pe)
Kya seekha? Har measuring cylinder par nishaan isi tarah tay matra ke liquid se lagaaye jaate hain. Tumhara cylinder thoda kam sateek hoga, par tareeka wahi hai.
Rasoi ka scale aksar 1 g se kam nahi naap paata, toh ek daana tolna mushkil hai. Ab 100 daane gin kar katori mein daalo (Tare karke) aur tolo. Jo mass aaye (lagbhag 2 g), use 100 se bhaag do. Ek daane ka mass lagbhag 0.02 g! Bahut chhoti cheez ko “dher mein tol kar bhaag do” wali chaal scientist bhi use karte hain.
Glass ya botal mein paani bharo jisme nishaan ho. Pehle khade hokar upar se reading padho, phir bilkul seedh mein baith kar, phir neeche se. Teeno reading likho. Kya teeno ek jaisi aayi? Isse samajh aayega ki aankh seedh mein rakhna kyun zaroori hai.
🧠 Think Like a Scientist
Sawaal: Golu aur Priya ne ek hi cylinder ki reading li. Golu ne 48 mL likha, Priya ne 46 mL. Dono ne cylinder ko chhua bhi nahi. Galti kahan hai?
Scientist ka tareeka dekho
1. Observe (dekho): ek hi paani, ek hi cylinder, phir bhi do alag reading.
2. Guess (anumaan): shayad dono ne alag-alag jagah se dekha. Golu khada tha, Priya baithi thi.
3. Test (jaanch): dono ek-ek karke upar se, seedh mein aur neeche se dekh kar reading lein aur likhein.
4. Result (nateeja): upar se dekhne par reading zyada aayi, seedh mein dekhne par dono ki reading 46 mL hi aayi.
5. Conclusion (nishkarsh): Golu upar se dekh raha tha, isliye uski reading galat thi. Sahi reading ke liye aankh meniscus ki seedh mein honi chahiye. Achha scientist naap ko do-teen baar dohra kar check karta hai.
🌍 Real Life Mein Mass aur Volume
- 🛒 Kirana aur sabzi ki dukaan: daal, chawal, sabzi taraazu par kg aur g mein tauli jaati hai.
- ⛽ Petrol pump: machine litre mein volume naapti hai, aur sarkaari vibhaag samay-samay par jaanch karta hai ki naap sahi hai.
- 🥛 Doodh ki thaili: par “500 mL” likha hota hai, yaani volume. Ghee ke dabbe par aksar “g” mein mass bhi likha hota hai.
- 💊 Dawai: syrup ka dose 5 mL ki chammach se, goli ka mass “mg” mein. Galat naap se dawai nuksaan kar sakti hai.
- 💍 Sunaar: sone ka ek-ek kan keemti hai, isliye bahut baareek digital balance use hota hai jo 0.001 g tak naapta hai.
- 🧑🍳 Rasoi: cake, laddoo jaisi cheezon mein sahi naap se hi swaad ek jaisa aata hai, bilkul Priya ki tarah!
🔁 Recap: Poora Post Ek Nazar Mein
- Andaaz nahi, tay units se naapo: mass g/kg/mg mein, volume mL/L/cm³ mein.
- Mass naapne ke liye beam balance ya digital balance. Bartan ka mass Tare se hatao ya ghatao.
- Liquid ka volume measuring cylinder se. Aankh seedh mein, meniscus ka sabse neeche wala hissa padho.
- Ek khaane ki value = do likhe numbers ka antar ÷ beech ke khaane.
- Regular solid ka volume = l × b × h.
- Irregular solid ka volume = V₂ − V₁ (displacement method); bada ho toh overflow can, tairta ho toh sinker.
- 1 kg = 1000 g, 1 g = 1000 mg, 1 L = 1000 mL, 1 mL = 1 cm³.
- Mass aur volume naap kar hi density (Mass ÷ Volume) nikaal sakte hain.
✍️ Fill in the Blanks
- Mass naapne ke liye ______ ka istemaal hota hai.
- Measuring cylinder mein liquid ki mudi hui upari satah ko ______ kehte hain.
- 1 mL = ______ cm³.
- Tedhi-medhi thos cheez ka volume ______ method se naapte hain.
- Digital balance par khaali bartan rakh kar ______ button dabane se screen 0 ho jaati hai.
- 3 kg = ______ g.
Answers
1) balance (taraazu) · 2) meniscus · 3) 1 · 4) displacement (paani hataane ka) · 5) Tare · 6) 3000
✅ True / False
- Paani ke meniscus ka sabse upar wala hissa padhna chahiye.
- 5 cm × 2 cm × 1 cm wale rubber ka volume 10 cm³ hai.
- Chaude beaker ke nishaan patle measuring cylinder se zyada sahi naap dete hain.
- Pathar daalne par paani 40 mL se 55 mL ho gaya, toh pathar ka volume 55 cm³ hai.
- 250 mg = 0.25 g.
- Namak ke dhele ka volume paani mein displacement se aasaani se naapa ja sakta hai.
Answers (kyun ke saath)
1) False: paani ke liye meniscus ka sabse neeche wala hissa, aankh seedh mein rakh kar padhte hain.
2) True: 5 × 2 × 1 = 10 cm³.
3) False: patle cylinder mein thode se liquid se bhi level saaf badalta hai, isliye woh zyada sateek hai; beaker ke nishaan lagbhag hote hain.
4) False: volume = 55 − 40 = 15 cm³; 55 toh paani + pathar dono ka hai.
5) True: 250 ÷ 1000 = 0.25 g.
6) False: namak paani mein ghul jaata hai, isliye paani ka level sahi badhottari nahi dikhayega.
🔘 MCQs
Q1. Liquid ka volume naapne ke liye kaunsa yantra sabse sahi hai? (a) Beam balance (b) Measuring cylinder (c) Thermometer (d) Scale (ruler)
✅ (b) Measuring cylinder: is par mL ke nishaan hote hain.
(a) balance mass naapta hai, volume nahi.
(c) thermometer taapmaan naapta hai.
(d) scale lambai naapta hai; liquid ki koi tay lambai-chaudai nahi hoti.
Q2. Measuring cylinder mein paani ki reading lene ka sahi tareeka kya hai? (a) Upar se dekh kar meniscus ka kinaara (b) Aankh seedh mein, meniscus ka sabse neeche wala hissa (c) Neeche se dekh kar meniscus ka neeche wala hissa (d) Kinaare aur beech ka ausat
✅ (b): paani ke liye yahi sahi niyam hai.
(a) kinaara upar chadha hota hai aur upar se dekhne par reading zyada aati hai.
(c) hissa sahi hai par neeche se dekhne par reading kam aati hai.
(d) aisa koi niyam nahi; isse galat reading aayegi.
Q3. Cylinder par 20 mL aur 30 mL ke nishaanon ke beech 5 khaane hain. Ek khaane ki value kya hai? (a) 5 mL (b) 1 mL (c) 2 mL (d) 10 mL
✅ (c) 2 mL: (30 − 20) ÷ 5 = 2 mL.
(a) 5 toh khaanon ki ginti hai, value nahi.
(b) 1 mL tab hota jab 10 khaane hote.
(d) 10 mL toh dono numbers ka poora antar hai.
Q4. Cylinder mein 35 mL paani tha. Pathar dubaane par level 47 mL ho gaya. Pathar ka volume? (a) 47 cm³ (b) 82 cm³ (c) 12 cm³ (d) 35 cm³
✅ (c) 12 cm³: 47 − 35 = 12 mL = 12 cm³.
(a) 47 paani + pathar dono ka hai.
(b) 82 = 47 + 35; jodna galat hai.
(d) 35 sirf paani ka volume hai.
Q5. 6 cm lamba, 5 cm chauda aur 2 cm ooncha dabba kitna volume gherta hai? (a) 13 cm³ (b) 60 cm³ (c) 30 cm³ (d) 600 cm³
✅ (b) 60 cm³: 6 × 5 × 2 = 60.
(a) 13 = 6 + 5 + 2; volume mein guna hota hai, jod nahi.
(c) 30 = 6 × 5; oonchai chhoot gayi.
(d) 600 hisaab ki galti hai (ek zero zyada).
Q6. 1.5 L kitna hai? (a) 15 mL (b) 150 mL (c) 1500 cm³ (d) 15000 mL
✅ (c) 1500 cm³: 1.5 × 1000 = 1500 mL = 1500 cm³.
(a) 1.5 × 10 kiya, galat.
(b) 1.5 × 100 kiya, galat.
(d) 1.5 × 10000 kiya, galat. 1 L = 1000 mL hi hota hai.
Q7. Khaali katori 120 g ki hai. Chawal daalne par balance 870 g dikhata hai. Chawal ka mass? (a) 990 g (b) 750 g (c) 870 g (d) 120 g
✅ (b) 750 g: 870 − 120 = 750 g.
(a) 990 = 870 + 120; katori ka mass jodna nahi, ghatana hai.
(c) 870 mein katori bhi shaamil hai.
(d) 120 sirf katori ka mass hai.
Q8. Paani mein tairne wale cork ka volume naapne ka sahi tareeka kaunsa hai? (a) Cork ko seedhe paani par chhod kar level ka badhna dekho (b) Sinker ke saath poora doobao, phir V₂ − V₁ (c) Cork ko balance par tolo (d) Use tairte hue overflow can mein daalo
✅ (b): sinker cork ko poora dooba deta hai; sinker ka volume alag se ghata dete hain.
(a) cork poora nahi doobta, isliye uska poora volume nahi dikhega.
(c) balance mass batata hai, volume nahi.
(d) tairta hua cork poora nahi dooba, isliye gira paani uska poora volume nahi hoga.
🔗 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: Measuring cylinder padhte waqt aankh meniscus ki seedh mein rakhni chahiye. R: Upar ya neeche se tirchi nazar se dekhne par reading galat aati hai.
✅ (a): tirchi nazar se galti hoti hai, isi wajah se aankh seedh mein rakhte hain. R, A ka sahi kaaran hai.
2. A: Pathar ka volume displacement method se naapa ja sakta hai. R: Pathar paani mein ghul jaata hai.
✅ (c): A sahi hai. R galat hai: pathar paani mein nahi ghulta, aur isi liye uska volume displacement se naap paate hain.
3. A: Digital balance ko samtal (flat) jagah par rakhna chahiye. R: Digital balance mass ko gram mein dikhata hai.
✅ (b): dono baatein sahi hain, par gram mein dikhana samtal rakhne ka kaaran nahi hai. (Asli kaaran: tedhi jagah par balance galat reading de sakta hai.)
📝 Very Short Answer (1 mark)
1. Meniscus kise kehte hain?
Measuring cylinder mein liquid ki mudi hui upari satah ko.
2. Mass ki SI unit kya hai?
Kilogram (kg).
3. 1 L mein kitne cm³ hote hain?
1000 cm³ (kyunki 1 L = 1000 mL aur 1 mL = 1 cm³).
4. Seedhe aakaar wale dabbe ka volume nikaalne ka formula likho.
Volume = lambai × chaudai × oonchai.
5. Least count kya hota hai?
Kisi yantra se naapa ja sakne wala sabse chhota hissa (jaise cylinder ke ek khaane ki value).
📝 Short Answer (2–3 marks)
1. Displacement method ke steps likho.
(i) Measuring cylinder mein itna paani lo ki cheez poori doob sake; reading V₁ lo. (ii) Cheez ko dhaage se baandh kar dheere se poora dubao. (iii) Nayi reading V₂ lo. (iv) Volume = V₂ − V₁. Jaise 50 mL se 62 mL hua, toh volume 12 cm³.
2. Bartan mein rakhi cheez ka mass naapne ke do tareeke batao.
(i) Tare: khaali bartan rakh kar Tare dabao, screen 0 ho jaayegi, phir cheez daalo; jo reading aaye woh sirf cheez ka mass hai. (ii) Ghatao: bartan ka mass alag tolo, phir bartan + cheez tolo, aur antar nikaalo. Jaise 650 − 150 = 500 g.
3. Liquid naapne ke liye patla measuring cylinder chaude beaker se behtar kyun hai?
Patle cylinder mein thoda sa liquid badhne par bhi level kaafi upar chadhta hai, isliye chhota antar bhi saaf padha ja sakta hai aur nishaan bhi baareek hote hain. Chaude beaker mein level bahut kam badalta hai, isliye uske nishaan sirf lagbhag naap dete hain.
4. Meniscus padhte waqt kin baaton ka dhyaan rakhna chahiye?
Cylinder samtal mez par ho; aankh meniscus ki seedh mein ho; paani jaise liquid ke liye meniscus ka sabse neeche wala hissa padho (paara/mercury jaise liquid mein satah upar ko ubhri hoti hai, wahan sabse upar wala hissa); reading do baar check karo.
📝 Long Answer (5 marks)
1. Ek tedhe-medhe pathar ka mass aur volume kaise naapoge? Saavdhaaniyan bhi likho. Agar mass 39 g aur volume 15 cm³ aaye toh density kya hogi?
Mass: digital balance ko samtal jagah rakho, 0 check karo, pathar rakh kar reading lo.
Volume (displacement): measuring cylinder mein paani lo aur aankh seedh mein rakh kar meniscus ke neeche wale hisse ki reading V₁ lo. Pathar ko dhaage se baandh kar dheere se poora dubao. Nayi reading V₂ lo. Volume = V₂ − V₁.
Saavdhaaniyan: pathar upar se mat girao (chheente aur cylinder tootne ka dar); pathar poora dooba ho; koi hawa ka bulbula na phanse; reading seedh mein lo; balance samtal ho.
Density: 39 ÷ 15 = 2.6 g/cm³, jo paani (1 g/cm³) se zyada hai, isliye pathar doobta hai.
2. In chaaron ka volume kaise naapoge, udaharan ke saath samjhao: (a) doodh (b) maachis ki dibbi (c) lohe ki chaabi (d) cork.
(a) Doodh (liquid): measuring cylinder mein daalo, meniscus ka neeche wala hissa aankh seedh mein rakh kar padho, jaise 100 mL.
(b) Maachis ki dibbi (regular solid): scale se l, b, h naapo aur guna karo; jaise 5 × 3.5 × 1.5 = 26.25 cm³.
(c) Chaabi (irregular, doobne wali): displacement: 30 mL se 33 mL, toh volume 3 cm³.
(d) Cork (tairne wala): sinker ke saath: sirf sinker doobane par 45 mL, sinker + cork par 57 mL, toh cork ka volume 57 − 45 = 12 cm³.
📰 Case-Based Question
Science period mein Ritu ki teacher ne use chaar ek jaisi steel ki goliyaan (balls) di. Ritu ne pehle chaaron ko digital balance par ek saath tola: screen par 62.4 g aaya. Phir usne measuring cylinder mein 60 mL paani liya aur chaaron goliyaan dheere-dheere usme daal di. Paani ka level 68 mL ho gaya. Ritu muskurayi: “Ab main ek goli ka mass aur volume dono bata sakti hoon!”
Q1. Chaaron goliyon ka kul volume kitna hai?
68 − 60 = 8 mL = 8 cm³.
Q2. Ek goli ka volume kitna hai?
8 ÷ 4 = 2 cm³.
Q3. Ek goli ka mass kitna hai?
62.4 ÷ 4 = 15.6 g.
Q4. Steel ki density kya aayi, aur goliyaan paani mein kyun doobi?
Density = 62.4 ÷ 8 = 7.8 g/cm³ (ya 15.6 ÷ 2 = 7.8). Yeh paani ki density (1 g/cm³) se bahut zyada hai, isliye goliyaan doob gayi.
🚀 HOTS
1. Ek pathar itna bada hai ki measuring cylinder ke munh mein nahi jaata. Uska volume kaise naapoge?
Overflow can se: nali wale bartan ko nali tak paani se bharo, neeche khaali measuring cylinder rakho, phir pathar dheere se poora dubao. Jitna paani nali se bah kar cylinder mein aaya, wahi pathar ka volume hai. (Bada bartan ho toh ek nishaan wala bada jug bhi chalega.)
2. Chheeni ke ek cube (sugar cube) ka volume kaise naapoge, jabki woh paani mein ghul jaata hai?
Do raaste: (i) cube ka aakaar seedha hai, toh scale se l × b × h naap lo. (ii) Displacement karna ho toh aisa liquid lo jisme chheeni na ghule (jaise khaane ka tel), aur usme V₂ − V₁ naapo.
3. Ek 1 L ki botal mein 1 kg paani aata hai. Kya usi botal mein bhara sarson ka tel bhi 1 kg hoga?
Nahi. Volume dono ka 1 L hai, par tel ki density (lagbhag 0.91 g/mL) paani se kam hai. Toh 1 L tel ka mass lagbhag 910 g hoga. Barabar volume ka matlab barabar mass nahi!
🏆 Olympiad Corner
1. Cylinder mein 50 mL paani hai. 10 ek jaise kanche daalne par level 74 mL ho jaata hai. Har kanche ka mass 6 g hai. Ek kanche ka volume aur density batao.
10 kanchon ka volume = 74 − 50 = 24 cm³, toh ek kanche ka = 24 ÷ 10 = 2.4 cm³. Density = 6 ÷ 2.4 = 2.5 g/cm³.
2. Cylinder mein 40 mL paani hai. Sirf sinker doobane par 45 mL, aur sinker + cork doobane par 57 mL. Cork ka mass 2.88 g hai. Cork ka volume aur density batao.
Cork ka volume = 57 − 45 = 12 cm³ (sinker ka volume 45 − 40 = 5 cm³ alag hai). Density = 2.88 ÷ 12 = 0.24 g/cm³, isliye cork tairta hai.
3. Ek paani ki tanki 2 m lambi, 1 m chaudi aur 0.5 m oonchi hai. Usme kitne litre paani aayega?
Volume = 2 × 1 × 0.5 = 1 m³. Aur 1 m³ = 1000 L, toh tanki mein 1000 litre paani aayega.
Har option pe tap karo, turant pata chalega sahi ya galat.
Q1. Empty bowl ka mass 180 gram. Flour daalne pe balance 730 gram dikhata hai. Flour ka mass?
(a) 550 gram
✅ Sahi! Flour = total − bowl = 730 − 180 = 550 gram. (Ya bowl rakh ke Tare dabao.)
(b) 910 gram
❌ Galat: Bowl ka mass add kar diya: 730 + 180 = 910. Bowl subtract karo: 730 − 180 = 550.
(c) 730 gram
❌ Galat: Total hi de diya (730), bowl nahi hataya. Flour = 730 − 180 = 550.
(d) 180 gram
❌ Galat: Bowl ka mass de diya (180). Flour = 730 − 180 = 550.
Q2. Measuring cylinder pe 30 mL aur 50 mL ke marks (nishaan) ke beech 10 divisions (do marks ke beech ki chhoti jagah) hain. Ek division kitne mL ka?
(a) 20 mL
❌ Galat: Sirf difference de diya: 50 − 30 = 20. Divisions se divide karo: 20 ÷ 10 = 2.
(b) 2 mL
✅ Sahi! Do likhe numbers ka difference ÷ divisions = (50 − 30) ÷ 10 = 20 ÷ 10 = 2 mL.
(c) 5 mL
❌ Galat: Bade number ko divide kiya: 50 ÷ 10 = 5. Difference lo: (50 − 30) ÷ 10 = 2.
(d) 3 mL
❌ Galat: Chhote number ko divide kiya: 30 ÷ 10 = 3. Difference lo: (50 − 30) ÷ 10 = 2.
Q3. Measuring cylinder mein 52 mL water tha. Stone poora dubaane pe level 70 mL ho gaya. Stone ka volume?
(a) 122 cm³
❌ Galat: Dono readings add kar di: 70 + 52 = 122. Stone ka volume = 70 − 52 = 18.
(b) 70 cm³
❌ Galat: Baad wali reading de di (70): ismein water bhi hai. Stone = 70 − 52 = 18.
(c) 18 cm³
✅ Sahi! Displacement: volume = baad − pehle = 70 − 52 = 18 mL, yaani 18 cm³ (1 mL matlab 1 cm³).
(d) 52 cm³
❌ Galat: Pehle wali reading de di (52): yeh sirf water hai. Stone = 70 − 52 = 18.
Q4. Cork float karta hai, isliye sinker use kiya. Cylinder mein 50 mL water; sinker dubaane pe 64 mL; sinker + cork dubaane pe 79 mL. Cork ka volume?
(a) 29 cm³
❌ Galat: Sinker ka volume bhi gin liya: 79 − 50 = 29. Sinker wali reading (64) subtract karo: 79 − 64 = 15.
(b) 14 cm³
❌ Galat: Sinker ka volume de diya: 64 − 50 = 14. Cork = 79 − 64 = 15.
(c) 143 cm³
❌ Galat: Readings add kar di: 79 + 64 = 143. Cork = 79 − 64 = 15.
(d) 15 cm³
✅ Sahi! Cork = (sinker + cork) − sinker = 79 − 64 = 15 cm³.
Q5. Ek medicine tablet pe 250 mg likha hai. Gram mein kitna?
(a) 0.25 gram
✅ Sahi! 1 gram mein 1000 mg. To 250 ÷ 1000 = 0.25 gram.
(b) 250000 gram
❌ Galat: Divide ki jagah multiply: 250 × 1000 = 250000. mg se gram: 250 ÷ 1000 = 0.25.
(c) 2.5 gram
❌ Galat: 100 se divide kiya: 250 ÷ 100 = 2.5. 1 gram mein 1000 mg: 250 ÷ 1000 = 0.25.
(d) 25 gram
❌ Galat: 10 se divide kiya: 250 ÷ 10 = 25. Sahi: 250 ÷ 1000 = 0.25.
📚 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 humne seekha ki andaaz se nahi, sahi naap se kaam banta hai. Aur Golu ke tedhe-medhe pathar ka volume bhi nikal aaya, bas thoda sa paani aur ek chhoti si chaal chahiye thi!
Beta, zindagi mein bhi kai sawaal “tedhe-medhe” lagte hain, jinka koi seedha formula nahi dikhta. Ghabraao mat. Thoda ruk kar socho, koi naya tareeka dhoondho, aur apni mehnat ko roz thoda-thoda “naapte” raho: aaj kitna padha, kal se kitna aage badhe. Jo apni pragati naapta hai, woh zaroor aage badhta hai. 📏✨
— CharuMam
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