Work, Energy, and Simple Machines: Class 9 Science Chapter 7 Hinglish mein

Exploration · Hinglish notes, simulations aur practice · Official NCERT chapter PDF ↗

Published 16 Oct 2026 · Updated 16 Oct 2026

100 min
31 practice questions
31 MCQs

Is chapter mein aap kya seekhenge

Constant force ka work W = F × s se calculate karna, aur tay karna ki work kab positive, negative ya zero hota hai
Force–displacement graph ke neeche ke area se work nikaalna
Work–energy theorem batana aur uski madad se kiye gaye work ko energy ke change se jodna
Energy ke main forms ke naam batana aur energy ka ek form se doosre form mein badalna trace karna
K = ½mv² aur U = mgh derive karke use karna, aur girne, slide karne aur pendulums par mechanical energy ka conservation apply karna
P = W/t se average power calculate karna aur watt ka use karna
Samjhana ki pulleys, inclined planes aur levers kaam ko kaise aasaan banate hain, aur unka mechanical advantage calculate karna

NCERT Science Class 9, Chapter 7, pp. 116–139 par based original companion text. Yeh NCERT se juda nahi hai aur NCERT ne ise endorse nahi kiya hai.

Ek water park mein teen slides ek hi tower se shuru hoti hain. Ek lagbhag seedhi neeche girti hai, ek smooth curve mein ghoom kar aati hai, aur ek lambe spiral mein mudti hai. Teeno se riders tezi se nikal kar ek hi pool mein girte hain. Kaun si slide sabse tez splash deti hai? Kya bhaari rider halke rider se zyada tez nikalta hai?

Tum in sawaalon ko Chapters 4 aur 6 ke forces aur equations of motion se solve karne ki koshish kar sakte ho. Lekin curving slide par rider par lagne wala push har pal direction badalta hai, aur calculation jaldi hi bhaari ho jaati hai. Yeh chapter tumhe ek shortcut deta hai: work, energy aur power ke ideas. Motion ki har detail follow karne ki jagah tum energy ka hisaab rakhte ho, bilkul waise hi jaise wallet mein paison ka hisaab rakhte hain.

Har activity apni energy kahin na kahin se leti hai. Tumne jo dal-chawal khaaya, woh school tak cycle chalate waqt tumhare pairon ko energy deta hai. Electricity mixer ke blades ghumati hai. Jalti LPG pressure cooker ko garam karti hai. Chapter mein aage tum simple machines se miloge: pulleys, ramps aur levers jo bhaari kaam ko halka mehsoos karaate hain, lekin tumhe kabhi free energy nahi dete.

7.1 Constant Force se kiya gaya Work

Roz ki baat-cheet mein work koi bhi aisi cheez hai jismein mehnat lagti hai: homework, dukaan par lambi shift, yahan tak ki line mein khade rehna bhi. Science is word ko kahin zyada narrow meaning mein use karta hai. Koi force kisi object par work (कार्य) tabhi karta hai jab object us force ki line ke along move kare. Abhi ke liye hum cheezon ko simple rakhte hain: force constant rehta hai, aur object uske along ek seedhi line mein chalta hai.

Work ko kaise naapa jaaye? Ek railway porter ke baare mein socho jise har kaam ke hisaab se paise milte hain. Do guna bhaari suitcase ko usi rack par uthana saaf taur par do guna kaam hai. Usi suitcase ko ek ki jagah do manzil seedhiyan chadh kar le jaana bhi do guna kaam hai. Science bhi work ko isi fair tarike se naapta hai: yeh force ke proportion mein badhta hai, aur force ke along chali gayi distance ke proportion mein bhi.

Definition

Constant force se kiya gaya work

Force ko, force ki direction mein hue object ke displacement se multiply karne par jo milta hai.

ExampleEk steady $50 N$ ka push jo cart ko $4 m$ aage le jaata hai, cart par $200 J$ work karta hai.

Constant force se kiya gaya work

W = F \times s

(7.2)

jahan

$W$: kiya gaya work (joules, J)
$F$: constant force (newtons, N)
$s$: force ke along displacement (metres, m)

Force aur displacement kisi bhi taraf point kar sakte hain: floor ke along, shelf se seedha upar, ramp ke neeche. Zaroori yeh hai ki dono ek hi line mein hon. Jab tum work describe karo, to hamesha batao ki kaun sa force (ya agent) work kar raha hai aur kis object par: porter ka lifting force suitcase par work karta hai.

Work ki SI unit joule (J) hai. Ek joule woh work hai jo tab hota hai jab $1 N$ ka force kisi object ko force ke along $1 m$ move karta hai, isliye $1 J = 1 N m .$ Kyunki $1 N = 1 k g m s^{- 2},$ ek joule yeh bhi hai: $1 k g m^{2} s^{- 2} .$ Iska size samajhne ke liye: $100 g$ ke ek apple ko $1 m$ upar uthane mein lagbhag ek joule lagta hai.

Graph se yeh idea aasaani se dikhta hai. Vertical axis par force aur horizontal axis par displacement plot karo. Constant force ek flat line deta hai, aur kiya gaya work uske neeche bane rectangle ka area hota hai: height × width = force × displacement (Fig. 7.1). Yahi rule tab bhi lagta hai jab object ke move karte waqt force badalta hai. Kiya gaya work phir bhi force–displacement graph ke neeche ka area hi hota hai, graph ki shape chahe jo bhi ho.

2/4Usi $2 m$ par $400 N$ : do guna uncha, isliye do guna work, $800 J .$

Fig. 7.1Force–displacement graph ke neeche ka area kiye gaye work ke barabar hota hai.NCERT Fig. 7.4 · p. 118

Force (newtons mein, 0 se 400 tak) ka displacement (metres mein, 0 se 4 tak) ke against graph. Pehle step mein 200 N uncha aur 2 m chauda rectangle shaded hai aur us par 400 J likha hai. Doosre step mein rectangle 400 N uncha aur 2 m chauda hai, us par 800 J likha hai, aur pehla rectangle dashed outline mein dikhta hai. Teesre step mein yeh 200 N uncha aur 4 m chauda hai, yeh bhi 800 J. Aakhri step mein ek triangle 3 m mein 0 N se 400 N tak uthta hai, us par 600 J likha hai.

7.1.1 Kiya gaya work kab zero hota hai?

Phir se dekho: $W = F \times s .$ Product zero hota hai agar koi bhi factor zero ho. “Force ke along” words mein ek aur case chhupa hai. Isliye teen situations mein force koi work nahi karta (Fig. 7.2).

Koi displacement nahi ( $s = 0$ ). Brakes lagakar khade ek bhare hue truck ko poori taakat se dhakelo. Truck zara bhi nahi hilta, isliye tumhara push us par koi work nahi karta.
Force motion ke right angle par. Ek waiter tray ko ek steady height par rakh kar hall ke paar le jaata hai. Uska haath tray ko upar push karta hai, lekin tray sideways move karti hai. Woh upward force tray par koi work nahi karta.
Motion ke along koi force nahi ( $F = 0$ ). Smooth ice par fisalti hockey puck chalti rehti hai, phir bhi koi use aage push nahi karta. Fisalte waqt us par koi work nahi hota.

To phir truck ko dhakelne ke baad tum thake hue kyun mehsoos karte ho? Push banaye rakhne ke liye tumhari muscles har second kai baar kasti aur dheeli hoti hain. Ismein tumhare khaane se mili energy use hoti hai, jo aakhir mein tumhari body ko garam karti hai. Tumne energy use ki hai, lekin truck par koi work nahi kiya. Kisi aur angle par lagne wale force ka work nikaalne ke liye thodi trigonometry chahiye, jo higher classes mein aayegi.

2/3Tray par upward force uske motion ke right angle par hai, isliye woh koi work nahi karta.

Fig. 7.2Teen tarike jinmein force koi work nahi karta.NCERT Figs. 7.5, 7.6 · p. 118

Teen scenes, har step mein ek. Pehle, ek insaan ek bade khade truck ke peeche jhuk kar use dhakel raha hai; ek force arrow truck ki taraf point karta hai, aur label par s = 0 likha hai kyunki truck nahi hilta. Doosre, ek waiter tray ko seedha pakde hue hai; ek alag sketch mein upward force arrow F aur sideways displacement arrow s ek right-angle mark par milte hain, jis par 90 degrees likha hai. Teesre, ek hockey puck ice ki patti par displacement arrow ke saath fisalti hai, aur label par likha hai ki s ke along F = 0.

7.1.2 Positive aur negative work

Force aur displacement dono ki directions hoti hain. Work in dono ko jod kar ek single number banata hai jiski koi direction nahi hoti, lekin uska ek sign hota hai: positive, negative ya zero.

Agar object usi taraf move kare jis taraf force lagta hai, to force positive work karta hai. Supermarket ki bhari trolley ko aage push karta shopper us par positive work karta hai. Agar object force ke opposite move kare, to force negative work karta hai. Lurhakti luggage trolley ko rokne wala railway porter use peeche ki taraf push karta hai jabki woh abhi bhi aage chal rahi hai, isliye woh trolley par negative work karta hai (Fig. 7.3).

Forces pairs mein aate hain (Newton's third law). Jab porter trolley ko peeche push karta hai, trolley uske haathon ko aage push karti hai, aur uske haath us forward direction mein thoda sa khisak jaate hain. Isliye jis pal porter trolley par negative work karta hai, usi pal trolley porter par positive work karti hai.

2/3Porter ka force peeche ki taraf point karta hai jabki trolley aage move karti hai: trolley par negative work.

Fig. 7.3Work ka sign is baat par depend karta hai ki force aur displacement ek hi taraf point karte hain ya nahi.NCERT Fig. 7.7 · p. 119

Do boxes se ladi ek luggage trolley platform par hai, saath mein right ki taraf point karta dashed displacement arrow s hai. Pehle step mein uske peeche ek shopper push karta hai, aur force arrow F bhi right ki taraf point karta hai: positive work. Doosre step mein ek porter uske saamne khada hai; force arrow F left ki taraf, displacement ke against point karta hai: negative work. Teesre step mein ek green arrow dikhata hai ki trolley porter ke haathon ko aage push karti hai, aur labels par likha hai: trolley par minus 60 J, porter par plus 60 J.

Example 7.1NCERT Example 7.1 · p. 119

Kuen se upar aur neeche

Ek ladki gaon ke kuen se paani ki balti upar kheenchti hai, rassi ko ek haath ke baad doosre haath se kheench kar. Baad mein woh khaali balti ko dheere-dheere wapas neeche utaarti hai, aur rassi ko rok kar rakhti hai jab woh uske haathon se fisalti hai. Har case mein balti par uske pull ka work positive hai ya negative? Aur gravity ke work ka kya?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 7.2NCERT Example 7.2 · p. 119

Luggage trolley ko rokna

Ek porter lurhakti luggage trolley ko peeche ki taraf push karke rokta hai; uska steady force hai $120 N .$ Rukte-rukte trolley $0.5 m$ aage chalti hai. Porter trolley par kitna work karta hai? Trolley porter par kitna work karti hai?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 2 questions

Ruko aur socho: answers ke saath

Short answerEasyPause and Ponder Q1
Ek coolie train ka intezaar karte hue platform par do minute tak bina hile khada rehta hai, sir par $20 k g$ ka trunk balance karke. Woh trunk par kitna work karta hai? Phir bhi woh thakta kyun hai?
Solution dikhao
AnswerTrunk par zero work; phir bhi use pakde rakhne mein uski muscles energy use karti hain.
Trunk nahi hilta, isliye $s = 0$ aur $W = F \times 0 = 0.$ Uska upward force us par koi work nahi karta. Load sambhale rakhne ke liye uski gardan, peeth aur pairon ki muscles ko lagataar kasna padta hai. Ismein uske khaane se mili energy use hoti hai, jo uski body mein heat ban jaati hai.
Quick answerEasyPause and Ponder Q2
Tum ek kitaab ko table par dhakelte ho. Haath se chhootne ke baad woh fisalti hai aur ruk jaati hai. Fisalte waqt friction kitaab par kis tarah ka work karta hai?
positive worknegative workzero work
Answer dekho
Answer (B) negative work
Friction peeche ki taraf lagta hai jabki kitaab aage move karti hai. Force aur displacement opposite hain, isliye friction negative work karta hai, aur isi wajah se kitaab ki speed kam hoti hai.

Quick check

4 mein se 1

Ek thele wala apne handcart ko seedhi sadak par

150 N

ke steady force se, push ki direction mein

40 m

tak dhakelta hai. Uska push cart par kitna work karta hai?

Answer dekho

Answer 6000 J

W = 150 N \times 40 m = 6000 J .

7.2 Work-Energy Theorem

Jhoolta hathoda plank mein keel thok deta hai. Chhat ki tanki mein rakha paani bahut neeche ek tap se tezi se nikalta hai. Chaabi bhari toy car floor par ghoomti hui chalti hai. In sab mein se har ek kisi aur cheez ko push karke move kar sakta hai: har ek work kar sakta hai. Jo bhi cheez work kar sakti hai, uske paas energy (ऊर्जा) hoti hai. Energy work karne ki capacity hai.

Yeh capacity kahan se aayi? Har case mein pehle kisi cheez ne object par work kiya. Hathoda ghumate waqt tumhari baanh ne us par work kiya. Pump ne paani ko tanki tak upar uthane mein work kiya. Tumhari ungliyon ne spring ko wind karne mein work kiya. Object par kiya gaya positive work uski energy badhata hai. Baad mein object kisi aur cheez par work karke energy aage de sakta hai. Jab hathoda keel par lagta hai, to woh keel ko lakdi mein ghusa deta hai aur dheema ho jaata hai: uski energy keel aur lakdi mein chali jaati hai (Fig. 7.4).

2/3Hathoda keel ko lakdi mein push karta hai (keel par positive work), jabki keel hathode ko wapas push karti hai (us par negative work).

Fig. 7.4Work energy ko tumhari baanh se hathode tak, aur hathode se keel tak pahunchata hai.NCERT Fig. 7.8 · p. 120

Lakdi ke plank mein ek keel seedhi khadi hai, aur uske upar ek hathoda pakda hua hai. Pehle step mein hathoda upar utha hai, ek dashed arc uska swing dikhata hai, aur labels par likha hai: baanh work karti hai, hathoda kinetic energy paata hai. Doosre step mein hathode ka head keel par aa gaya hai aur use lakdi mein aur gehra ghusa diya hai; labels par likha hai keel par plus work aur hathode par minus work. Teesre step mein hathoda keel par tika hai, aur label kehta hai ki energy ab keel, lakdi aur heat mein hai.

TheoremWork-energy theorem

Kisi object par kiya gaya work uski energy ke change ke barabar hota hai.

W = E_{final} - E_{initial}

(7.3)

jahan

$W$: object par kiya gaya work (J)
$E_{initial}, E_{final}$: pehle aur baad mein uski energy (J)

Yeh ek bahut general result hai. Yeh un forces ke liye bhi kaam karta hai jo object ke move karte waqt badalte hain, aur objects ke poore systems ke liye bhi, jaise aapas mein jude wagons wali train. Aur kyunki work joule-for-joule energy mein badalta hai, energy ko bhi work wali unit mein hi naapte hain: joule.

Example 7.3NCERT Example 7.3 · p. 120

Marbles ki chain

Marbles (kanche) ke khel mein Ravi apni shooter marble ko ungli se flick karta hai. Woh lurhak kar doosri marble se takraati hai, jo aage lurhak kar teesri se takraati hai. Har stage par batao ki kaun kis par work karta hai, aur har marble ki energy kaise badalti hai.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 1 question

Ruko aur socho: answers ke saath

Short answerMediumPause and Ponder Q3
Tum seedhi sadak par zor se pedal maarte ho, phir pedal karna rok kar red light par brake lagakar ruk jaate ho. Har stage par tumhari muscles ki energy kahan jaati hai?
Solution dikhao
Pedal karna: tumhare khaane ki chemical energy tumhari aur cycle ki kinetic energy ban jaati hai. Iska kuch hissa tumhari body ko garam karta hai, aur kuch hissa air resistance aur tyres aur chain ke friction ke against use hota hai, jo aakhir mein heat aur thodi sound ban jaata hai.
Brake lagana: brakes cycle par negative work karte hain. Uski kinetic energy brake pads aur rims, tyres aur sadak mein heat ban jaati hai.

Quick check

3 mein se 1

Ruki hui toy car ko smooth floor par push karne se woh

3 J

energy paati hai. Tumhare push ne us par kitna work kiya?

0 J

1.5 J

3 J

6 J

Answer dekho

Answer (C) $3 J$

Work–energy theorem ke hisaab se kiya gaya work energy mein hue gain ke barabar hai, yaani

3 J .

Theorem mein khud koi ½ ka factor nahi aata.

7.3 Energy ke Forms

Ab tak hamari energy chalte ya upar uthaye gaye objects ki thi: mechanical energy. Lekin energy kai aur forms mein bhi milti hai, aur woh lagataar ek form se doosre form mein badalti rehti hai. Table 7.1 mein main forms roz ki misaalon ke saath diye gaye hain.

Table 7.1Energy ke formsNCERT Fig. 7.10 · p. 121

Form	Kahan milti hai	Roz ki misaal
Mechanical	chalte objects mein, aur upar uthaye ya dabaaye gaye objects mein	chalti bus; dam ke peeche ruka paani
Chemical	khaane aur fuels mein atoms ke judne ke tarike mein band	dal aur chawal, LPG, torch ka cell
Electrical	circuit mein ghumaye jaate charges mein	ceiling fan chalane wala current
Thermal	kisi substance ke hilte-dulte particles mein; garam hone par zyada	garam press (iron)
Light	radiation ke roop mein chalti hai, khaali space mein bhi	solar panel par padti sunlight
Sound	hawa, paani ya solids mein vibrations ke roop mein chalti hai	dhol ki thaap
Nuclear	tab nikalti hai jab atoms ke centres tootte ya judte hain	Sun; nuclear power station

Devices energy changers hote hain. Torch apne cells ki chemical energy ko electrical energy mein, aur phir light mein badalti hai. Mixer-grinder electrical energy ko apne ghoomte blades ki kinetic energy mein badalta hai. Chhat par laga solar water heater light ko thermal energy mein badalta hai. Tum bhi energy changer ho: seedhiyan chadhte waqt tum khaane ki chemical energy ko potential energy mein badalte ho. Lagbhag har badlaav mein kuch heat bhi nikalti hai, isiliye phone charger garam lagta hai.

4/4Ghar mein lamp electrical energy ko light mein badalta hai, saath mein thodi heat bhi.

Fig. 7.5Ek energy chain: dam ke peeche ruke paani se ghar ki light tak.

Left mein oonchi zameen par dam ke peeche paani ka reservoir hai. Ek pipe tezi se neeche ek chhote power house tak jaata hai jismein turbine hai, aur ek wire aage ek ghar tak jaata hai jismein lamp hai. Pehle step mein ruke paani ke paas ek tag par potential likha hai. Doosre step mein paani pipe se neeche behta hai aur doosre tag par kinetic likha hai. Teesre step mein turbine ghoom gayi hai aur teesre tag par electrical likha hai. Chauthe step mein lamp jalta hai aur chauthe tag par light plus heat likha hai.

Ab se hum mechanical energy par focus karenge, kyunki yeh seedhe un forces aur motion se judi hai jinse tum Chapters 4 aur 6 mein mil chuke ho.

Quick check

2 mein se 1

Har device ko uske main energy change se match karo.

Left mein koi item tap karo, phir right mein uska match.

Answer dekho

Answer

solar cell : light → electrical
electric iron (press) : electrical → thermal
torch ka cell : chemical → electrical
loudspeaker : electrical → sound

Har device energy ka ek form leta hai aur doosra form deta hai; lagbhag hamesha kuch heat bhi banti hai.

7.4 Mechanical Energy

Kisi object ki mechanical energy (यांत्रिक ऊर्जा) is baat se aati hai ki woh kaise move kar raha hai aur kahan hai. Iske do hisse hain: kinetic energy, jo motion se aati hai, aur potential energy, jo position ya shape se aati hai. Har hisse ko number mein batane ke liye hum poochhte hain ki object ko woh energy dene mein kitna work lagta hai.

7.4.1 Kinetic energy

Phenka gaya pathar khidki ka sheesha tod sakta hai; tez bus car ko pichka sakti hai. Har chalti cheez mein kinetic energy (गतिज ऊर्जा) hoti hai, yaani motion ki energy. Ruke hue object mein yeh bilkul nahi hoti, isliye chalte object ki kinetic energy theek utna hi work hai jitna use rest se uski abhi ki speed tak laane mein laga (Fig. 7.6).

3/3Distance $s$ ke baad uski speed hai $v .$ Work $F \times s$ extra kinetic energy ban gaya hai.

Fig. 7.6Steady push se kiya gaya work extra kinetic energy ke roop mein dikhta hai.NCERT Fig. 7.11 · p. 121

Mass m ki ek cart seedhe track par khadi hai. Pehle step mein woh speed u se dheere chalti hai, jo ek chhote arrow se dikhayi gayi hai. Doosre step mein ek force arrow F use peeche se push karta hai aur woh thoda raasta tay kar chuki hai, thodi tez. Teesre step mein woh distance s chal chuki hai, jo ek dimension line se mark hai, aur ek lamba arrow uski nayi speed v dikhata hai. Ek label par likha hai: kiya gaya work W = F × s, yeh poora extra kinetic energy ban jaata hai.

DerivationObject ki speed badalne mein kiya gaya work

Mass $m$ ke object par uske motion ke along ek constant force $F$ lagta hai. Uski speed $u$ se badh kar $v$ ho jaati hai, aur is beech woh jo distance chalta hai woh hai $s .$ Constant force ka matlab hai constant acceleration, jise kehte hain $a,$ isliye Chapter 4 ki equations of motion yahan lagti hain. $v^{2} = u^{2} + 2 a s$ se shuru karo aur ise solve karke nikaalo $s :$

s = \frac{v^{2} - u^{2}}{2 a}

(7.4)

Kiya gaya work hai $W = F \times s,$ aur Newton's second law se milta hai $F = m a .$ Dono ko substitute karo:

W = m a \times \frac{v^{2} - u^{2}}{2 a}

W = \frac{1}{2} m v^{2} - \frac{1}{2} m u^{2}

(7.5)

Acceleration cancel ho jaata hai. Answer sirf shuruaati aur aakhri speeds par depend karta hai, is par nahi ki humne kitne zor se ya kitne halke se push kiya. Work–energy theorem ke hisaab se yeh work object ki energy ka change hai. Agar object rest se shuru kare ( $u = 0$ ), to kiya gaya work uski kinetic energy ke barabar hai, jab uski speed ho $v .$

Kinetic energy

K = \frac{1}{2} m v^{2}

(7.6)

jahan

$K$: kinetic energy (J)
$m$: mass (kg)
$v$: speed (m/s)

(7.5) se teen quick rules nikalte hain. Agar object par kiya gaya total work positive hai, to uski speed badhti hai aur woh kinetic energy paata hai; agar negative hai, to woh dheema hota hai aur kuch energy khota hai; agar zero hai, to uski speed nahi badalti. Kyunki $v$ ka square hota hai, kinetic energy speed ke saath tezi se badhti hai: speed double karo to kinetic energy chaar guna ho jaati hai. Isiliye $80 k m / h$ par crash kahin zyada bura hota hai; utna bura nahi hota jab speed ho $40 k m / h .$ Work ki tarah kinetic energy bhi ek scalar hai jise joules mein naapte hain.

Example 7.4NCERT Example 7.4 · p. 122

School zone mein dheema hona

School zone mein aate hue ek scooter $60 k m / h$ se dheema hokar $20 k m / h$ par aa jaata hai. (a) Uski kinetic energy ka kitna hissa bachta hai? (b) Ek doosre scooter ka mass do guna hai, aur uski speed bhi hai $20 k m / h .$ Uski kinetic energy pehle scooter ki kinetic energy se kaise compare hoti hai?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 7.5NCERT Example 7.5 · p. 122

Javelin ki kinetic energy

$800 g$ mass ka ek javelin athlete ke haath se is speed par nikalta hai: $108 k m / h .$ Uski kinetic energy nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 7.6NCERT Example 7.6 · p. 123

Kya car over-speeding kar rahi thi?

Ek car (mass $1200 k g$ ) seedhi sadak par zor se brake lagati hai, aur rukne tak itna chalti hai: $30 m .$ Tyre ke nishaan dikhate hain ki braking force poore samay lagbhag $4500 N$ tha. Speed limit hai $50 k m / h .$ Kya driver limit ke andar tha?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 2 questions

Ruko aur socho: answers ke saath

NumericalMediumPause and Ponder Q4
$1000 k g$ mass ki ek car aur $9000 k g$ mass ke ek loaded truck ki kinetic energy same hai. Kaun zyada tez chal raha hai, aur kitne guna tez?
Solution dikhao
AnswerCar, teen guna tez.
$\frac{1}{2} (1000) v_{car}^{2} = \frac{1}{2} (9000) v_{truck}^{2}$
$\frac{v_{car}^{2}}{v_{truck}^{2}} = 9$
Square root lene par, $v_{car} = 3 v_{truck} .$ Same kinetic energy rakhne ke liye halki gaadi ko zyada tez chalna padta hai.
Quick answerEasyPause and Ponder Q5
Steady $80 k m / h$ par chalti express train mein doosre station se guzarte waqt, pehle station ki tulna mein, zyada kinetic energy hoti hai.
SahiGalat
Answer dekho
Answer Galat
Kinetic energy sirf mass aur speed par depend karti hai, $K = \frac{1}{2} m v^{2},$ is par nahi ki train kahan hai. Same speed, same kinetic energy.

Quick check

3 mein se 1

0.45 k g

mass ki ek football ki speed hai

20 m / s .

Uski kinetic energy kitni hai?

Answer dekho

Answer 90 J

K = \frac{1}{2} \times 0.45 \times 20^{2} = 90 J .

7.4.2 Potential energy

Energy jama bhi rah sakti hai, use hone ka intezaar karte hue. Toy car ko chaabi bharo aur neeche rakho: woh khud hi bhaag nikalti hai. Toy dart gun mein dart daba kar daalo, to ek spring dab jaati hai; trigger dabao aur spring dart ko bahar phenk deti hai. Pole vaulter upar jaate waqt apna pole mod deti hai, aur jab woh seedha hota hai to use bar ke upar utha deta hai. Har case mein pehle kisi ne kisi cheez ki shape badalne ke liye work kiya, aur woh work us nayi shape mein jama ho gaya.

Dabi hui spring toy ko kyun phenk deti hai (Fig. 7.7)? Spring ke andar uske coils ke beech ke forces unhe aur paas dhakele jaane ko resist karte hain. Dabane ka matlab hai un forces ke against work karna, aur yeh work khota nahi: yeh spring ki nayi shape mein intezaar karta hai. Use chhodo, to wahi internal forces toy ko tab tak push karte hain jab tak spring apni natural length mein wapas na aa jaaye, aur stored energy kinetic energy ke roop mein de dete hain.

Aise objects ka group jo ek doosre ko kheenchte ya dhakelte hain, apne arrangement mein bhi energy store kar sakta hai. Floor se school bag uthao, to tum bag aur Earth ko unke aapasi pull ke against alag kar rahe ho; chhodo, to woh phir paas aa jaate hain. North pole ko south pole se zor lagakar alag karo, to tum unke attraction ke against work karte ho; chhodo, to woh itne zor se wapas chipakte hain ki ungli dab jaaye. Ek doosre ko attract ya repel karne wale charges bhi aise hi behave karte hain.

Definition

Potential energy

Stored energy jo is baat par depend karti hai ki system kaise arranged hai: kisi deformed object ki shape, jaise dabi hui spring, ya attract ya repel karne wale objects ki positions, jaise upar uthi ball aur Earth.

ExampleChhat ki tanki ke paani mein potential energy hoti hai kyunki woh taps se bahut upar hai.

1/2Har system par work kiya gaya hai, aur energy store hai.

Fig. 7.7Shape (spring) ya positions (magnets, ball aur Earth) ke change se stored energy.NCERT Figs. 7.14–7.16 · p. 124

Teen panels aamne-saamne, jin par spring, magnets, aur ball plus Earth likha hai. Pehle step mein ek spring deewar aur block ke beech dabi hai, bar magnets ka ek pair, jismein south pole north pole ki taraf hai, alag pakda hua hai, aur ek ball zameen se upar ek dashed height line par pakdi hui hai. Doosre step mein spring khul gayi hai aur block ko door dhakel diya hai, magnets paas aakar chhoo rahe hain, aur ball zameen par gir gayi hai; har ek ke saath motion dikhata arrow hai. Neeche ke labels par shape, positions aur positions likha hai.

Gravitational potential energy

Ball–Earth pair mein lagbhag saara moving ball karti hai: Earth soch se bhi zyada bhaari hai aur mushkil se hilti hai. Isiliye log seedha kehte hain “ball ki potential energy” (स्थितिज ऊर्जा). Is tarah height se stored energy gravitational potential energy hai. Is chapter mein aage hum sirf isi tarah ki potential energy calculate karenge, aur hamesha lenge $g = 10 m / s^{2} .$

Activity 7.1NCERT Activity 7.1 · p. 125

Aate ki tray mein gaddhe

Tumhe chahiye

ek gehri tray ya baking tin
aata ya mehin sookhi ret, lagbhag 5 cm gehri
ek bhaari steel ball ya bada stone marble (kancha)
ek metre scale aur ek chhota ruler

Pehle guess karo

Kis drop se sabse gehra gaddha banega?

25 cm se50 cm se100 cm sesab barabar gehre honge

Aate ko smooth karo taaki uski surface flat ho.
Ball ko surface se $25 c m$ upar pakdo aur girne do. Use dhyaan se bahar nikaalo.
Ab dohrao, pehle $50 c m$ se aur phir $100 c m,$ har baar aate ke ek naye, flat hisse par.
Har gaddhe mein ruler khada karke uski depth naapo, aur table bharo.

Table 7.2Aate mein gaddhe

Drop height	Tumhara prediction (rank 1–3)	Gaddhe ki depth (cm)
25 cm
50 cm
100 cm

Tumhari entries apne aap save hoti hain.

DerivationUpar uthaye gaye object ki potential energy

Zameen ko woh level maano jahan potential energy zero hai. Maano mass $m$ ke object ko dheere-dheere ek height tak uthana hai, jise kehte hain $h,$ to tumhe uske weight ke barabar force se upar push karna hoga, yaani $m g .$ Force displacement ke along lagta hai, isliye tumhara kiya gaya work hai force × distance, yaani $m g \times h :$

W = m g h

(7.7)

Work–energy theorem ke hisaab se yeh work object ki potential energy ke roop mein store hota hai, jab woh is height par ho: $h .$

Gravitational potential energy

U = m g h

(7.8)

jahan

$U$: potential energy (J)
$m$: mass (kg)
$g$: gravity ke kaaran acceleration, is chapter mein $10 m / s^{2}$
$h$: chune gaye zero level se height (m)

Iski unit bhi joule hi hai. Dhyaan do ki $U$ sirf is baat par depend karta hai ki object aakhir mein kitni height par hai, is par nahi ki woh wahan kis raaste se pahuncha.

Example 7.7NCERT Example 7.7 · p. 126

Loft par bag

Chawal ka $5 k g$ ka bag floor se uthakar $2.4 m$ oonche loft par rakha jaata hai. Woh kitni potential energy paata hai? Lo $g = 10 m / s^{2} .$

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 1 question

Ruko aur socho: answers ke saath

Short answerEasyPause and Ponder Q6
Ek delivery drone zameen se $20 m$ upar steady speed se level udta hai. Baad mein woh dheere-dheere, steadily upar uthkar is height tak jaata hai: $35 m .$ Flight ke har hisse mein uski potential energy kaise badalti hai?
Solution dikhao
Level flight: uski height rehti hai $20 m,$ isliye uski potential energy nahi badalti, chahe woh kitna bhi door ude.
Upar uthna: uski height badhti hai $15 m,$ isliye uski potential energy itni badhti hai: $m g \times 15 m .$

Quick check

3 mein se 1

2 k g

ka gamla floor se

1.5 m

upar ek shelf par rakha hai. Floor ko zero maano, to uski potential energy kitni hai? (

g = 10 m / s^{2}

)

Answer dekho

Answer 30 J

U = m g h = 2 \times 10 \times 1.5 = 30 J .

7.4.3 Mechanical energy ka conservation

Dono tarah ki energy jodo to mechanical energy milti hai: $E = K + U .$ Jab koi object freely girta hai, to iska kya hota hai? Chalo rest se giraye gaye ek pathar ka hisaab rakhte hain, air resistance ko ignore karke.

DerivationGirte object ki energy

Shuru mein, point A par, mass $m$ ka ek object rest par hai, aur uski height hai $h .$

\begin{aligned} K_{A} & = 0 \\ U_{A} & = m g h \\ E_{A} & = m g h \end{aligned}

(7.9)

Time $t$ tak girne ke baad woh point B par pahunchta hai. Uska acceleration hai $g,$ isliye uski speed hai $v = g t$ aur jitna woh gira hai woh distance hai $d = \frac{1}{2} g t^{2} .$ Ab uski height hai $h - d,$ aur uski kinetic energy hai $\frac{1}{2} m v^{2} = \frac{1}{2} m g^{2} t^{2} = m g d .$ Isliye B par energies, aur unka total $E_{B} = U_{B} + K_{B},$ yeh hain

\begin{aligned} U_{B} & = m g h - m g d \\ K_{B} & = m g d \\ E_{B} & = m g h \end{aligned}

(7.10)

Mili hui kinetic energy, $m g d,$ theek utni hi hai jitni potential energy khoyi. Total har pal $m g h$ hi rehta hai, neeche tak (Fig. 7.8).

2/3 $10 m$ par: $100 J$ potential aur $100 J$ kinetic.

Fig. 7.8Ball girte waqt potential energy kinetic energy mein badalti hai; total same rehta hai.NCERT Fig. 7.19 · p. 126

Left mein 1 kg ki ball 20 m par point A se girti hai, 10 m par point B se guzarti hai, aur zameen par point C tak pahunchti hai. Right mein teen bars potential energy, kinetic energy aur total dikhate hain. Pehle step mein ball A par rest mein hai: potential 200 J, kinetic 0 J. Doosre step mein woh B par lagbhag 14 m/s se chal rahi hai: potential 100 J aur kinetic 100 J. Teesre step mein woh C par 20 m/s se chal rahi hai: potential 0 J aur kinetic 200 J. Total bar poore samay 200 J par rehta hai.

LawMechanical energy ka conservation

Jab kisi object par sirf gravity hi work kar rahi ho, to uski mechanical energy $K + U$ constant rehti hai. Jitni potential energy khoti hai, utni kinetic energy milti hai, aur jitni kinetic energy khoti hai, utni potential energy milti hai.

Activity 7.2NCERT Activity 7.2 · p. 127

Kya bob wapas upar chadhta hai?

Tumhe chahiye

bob ke liye ek bhaari nut, chaabi ya chhota pathar
lagbhag 1 m mazboot dhaaga
deewar ya darwaze ki chaukhat par oonchi lagi keel ya hook
chart paper ki ek sheet aur tape
ek pencil aur ek ruler

Pehle guess karo

Doosri taraf bob upar jaayega

line se kaafi uparlagbhag line takline tak ka sirf aadha

Bob ko dhaage se baandho aur keel se latkao, taaki woh deewar ke paas, bina chhue jhool sake.
Bob ke peeche deewar par chart paper tape se chipkao. Bob ko ek taraf kheencho aur uske centre se hokar paper par ek level line kheencho.
Bob ko line par rest se chhodo; use push mat karo. Dekho ki doosri taraf woh kahan mudta hai.
1st, 5th aur 10th swing par note karo ki doosri taraf woh kitna upar uthta hai.

Table 7.3Woh kitna upar chadhta hai?

Swing	Doosri taraf bob mudta hai…
1st
5th
10th

Tumhari entries apne aap save hoti hain.

2/4Sabse tez chalta hua: saari kinetic energy.

Fig. 7.9Har swing mein potential aur kinetic energy aapas mein jagah badalti hain.NCERT Fig. 7.20 · p. 127

Ek support se pendulum latka hai, aur left mein bob ki shuruaati position se hokar ek dashed release level bana hai. Right mein do bars potential aur kinetic energy dikhate hain. Pehle step mein bob left end par release level par pakda hai: potential bar bhara hai aur kinetic bar khaali. Doosre step mein bob sabse neeche ke point par hai: potential khaali, kinetic bhara. Teesre step mein woh right end par hai, wapas release level par: potential phir se bhara. Chauthe step mein, kai swings baad, woh release level se neeche hi mud jaata hai aur potential bar sirf lagbhag aadha bhara hai, saath mein label hai ki har swing mein thoda neeche.

Mechanical energy ka conservation kuch mushkil problems ko kuch hi lines ki working mein badal deta hai. Chalo chapter ki shuruaat wale water-park sawaal ka answer dete hain.

Example 7.8NCERT Example 7.8 · p. 128

Water slide ke neeche speed

Ek water slide pool se $3.2 m$ upar se shuru hoti hai. Ek rider upar se rest se chalta hai, aur paani slide ko lagbhag frictionless bana deta hai. (a) Neeche rider kitni tezi se chal raha hai? (b) Kya do guna mass wala rider, ya same height se alag shape ki slide, answer badal degi? Lo $g = 10 m / s^{2} .$

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Shape phir bhi yeh tay karti hai ki ride kitni der chalti hai: jo slide shuru mein tezi se neeche girti hai, woh tumhe jaldi speed de deti hai. Ise, aur friction ke effect ko, neeche wali lab mein test karo.

InteractiveWater-slide energy lab

Tower se shuru hoti slide ka side view, upar ek rider ke saath. Buttons se straight, curved ya bumpy slide chuni jaati hai, sab same height se; sliders height ko 2 se 8 m tak aur rider ka mass 20 se 80 kg tak set karte hain; do buttons friction ko off (wet) ya on (dry) karte hain. Play dabane par rider neeche slide karta hai, jabki chaar bars potential energy, kinetic energy, heat aur total dikhate hain, aur readouts speed aur time dikhate hain. Neeche ek message final speed batata hai: friction ke bina har shape aur mass ke liye yeh 2gh ka square root hai, aur friction ke saath kam hai, aur heat mein badli energy bhi likhi hoti hai.

Fig. 7.10Slide ki shape, height aur rider ka mass chuno, phir Play dabao aur energy bars dekho.

Example 7.9NCERT Example 7.9 · p. 128

Roller coaster par braking run

$400 k g$ mass ki ek roller-coaster train (riders samet) ek uphill braking run mein is speed se ghusti hai: $12 m / s .$ Run ke along track har $4 m$ chalne par $1 m$ upar uthta hai, aur brake fins train ko is steady force se peeche push karte hain: $1000 N .$ Rukne se pehle train run ke along kitni door jaati hai? Lo $g = 10 m / s^{2} .$

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 2 questions

Ruko aur socho: answers ke saath

NumericalMediumPause and Ponder Q7
$0.3 k g$ ka ek amrood zameen se $5 m$ upar ki daal se girta hai. Air resistance ignore karke daal par, aadhe raaste mein, aur zameen par girne se theek pehle uski potential, kinetic aur total mechanical energy nikaalo. Lo $g = 10 m / s^{2} .$
Solution dikhao
Daal par, $U = m g h = 0.3 \times 10 \times 5 = 15 J$ aur $K = 0.$ Aadhe raaste mein height hai $2.5 m,$ isliye $U = 7.5 J$ aur baaki $7.5 J$ kinetic hai. Girne se theek pehle $U = 0$ aur $K = 15 J,$ yaani speed $10 m / s .$
Table 7.4
PE (J) KE (J) Total (J)
Daal par 15 0 15
Aadhe raaste 7.5 7.5 15
Girne se theek pehle 0 15 15
Total neeche tak $15 J$ (yaani $m g h$ ) hi rehta hai.
Short answerMediumPause and Ponder Q8
Ek science park mein ek ball ko humps ki ek line wale track ke upar se rest se chhoda jaata hai. Har hump pichhle wale se neecha hai. Ball ke lurhakte waqt energy ke changes describe karo, aur samjhao ki humps ko neecha kyun hona padta hai.
Solution dikhao
Slope se neeche lurhakte waqt potential energy kinetic energy ban jaati hai; agla hump chadhte waqt kinetic energy wapas potential energy ban jaati hai, isliye har hump ke top par ball sabse dheemi hoti hai. Friction aur air resistance lagataar thodi mechanical energy ko heat mein badalte rehte hain, isliye ball ka total ghatta rehta hai. Woh kabhi utna upar nahi chadh sakti jitne se shuru hui thi, isliye har hump pichhle se neecha hona chahiye, warna ball wapas lurhak jaayegi.

	PE (J)	KE (J)	Total (J)
Daal par	15	0	15
Aadhe raaste	7.5	7.5	15
Girne se theek pehle	0	15	15

Quick check

4 mein se 1

Ek pathar ko is height se giraya jaata hai:

20 m .

Air resistance ignore karo, to zameen se takraane se theek pehle woh kitni tezi se chal raha hai? (

g = 10 m / s^{2}

)

m/s

Answer dekho

Answer 20 m/s

\frac{1}{2} m v^{2} = m g h,

isliye

v = \sqrt{2 g h} = \sqrt{2 \times 10 \times 20} = 20 m / s .

7.5 Power

Do water pumps ek hi underground sump se ek jaisi chhat ki tankiyan bharte hain. Ek pump apni tanki 10 minute mein bharta hai; doosre ko 40 minute lagte hain. Dono same mass ka paani same height tak uthate hain, isliye dono same work karte hain. Tez pump zyada work nahi kar raha; woh work zyada jaldi kar raha hai. Work karne ki rate ko power (शक्ति) kehte hain.

Average power

P = \frac{W}{t}

(7.11)

jahan

$P$: average power (watts, W)
$W$: kiya gaya work (J)
$t$: laga hua time (s)

Power ko watts (W) mein naapte hain. Ek watt ka matlab hai har second ek joule work, $1 W = 1 J / s .$ Badi powers kilowatts mein di jaati hain, $1 k W = 1000 W .$ Same time mein zyada work, ya kam time mein same work, dono ka matlab hai zyada power (Fig. 7.11). Dhyaan rakho ki unit W (watt) ko work ke symbol $W$ ke saath mix mat karna.

3/3B ko lagte hain $60 s :$ $P = 3000 / 60 = 50 W .$ Same work, power sirf ek-chauthai.

Fig. 7.11Same work, alag time, alag power.

Do ek jaisi staircases, A aur B, dono 6 m oonchi. Ek label par likha hai: same chadhai, har ek 3000 J. Pehle step mein dono climbers neeche khade hain. Doosre step mein climber A top par pahunch gaya hai, labels 15 s aur 200 W ke saath, jabki climber B abhi pehli seedhi par hi hai. Teesre step mein B bhi top par pahunch gaya hai, labels 60 s aur 50 W ke saath.

Example 7.10NCERT Example 7.10 · p. 129

Chhat ki tanki bharna

Ek pump 4 minute mein $500 k g$ paani sump se $12 m$ oonchi tanki tak uthata hai. Uska power output kya hai? Lo $g = 10 m / s^{2} .$

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 7.11NCERT Example 7.11 · p. 129

E-rickshaw ki power

Passengers samet ek e-rickshaw ka mass hai $600 k g .$ Seedhi sadak par woh $8 s$ mein rest se $36 k m / h$ tak speed pakadta hai. Friction aur air resistance ignore karo, to uski motor average kitni power deti hai?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

40 k g

ki student

6 m

oonchi seedhiyan daud kar chadhti hai, aur use lagte hain

12 s .

Khud ko upar uthane mein woh kitni power lagati hai? (

g = 10 m / s^{2}

)

Answer dekho

Answer 200 W

W = m g h = 40 \times 10 \times 6 = 2400 J,

isliye

P = 2400 / 12 = 200 W .

7.6 Simple Machines

Agar paas mein ek takhta ho, to koi bhi bhara gas cylinder seedha delivery truck par nahi uthata, aur agar rassi chadhane ke liye ek pahiya ho, to koi bhi gehre kuen se balti haath-haath se nahi kheenchta. Aise tools kaam ko chhota nahi karte: cylinder ko phir bhi utni hi potential energy milti hai. Woh badalte hain tumhara lagaya force: use chhota karke, ya ek zyada aaramdeh direction mein mod kar. Aise devices simple machines (सरल मशीन) hain. Is section mein hum teen dekhenge: pulleys, inclined planes aur levers.

Do words madad karte hain. Effort woh force hai jo tum machine par lagate ho. Load woh force hai jise machine ko haraana hota hai, aksar uthaya ja raha weight. Inka ratio batata hai ki machine tumhare force ko kitna guna karti hai:

Mechanical advantage

MA = \frac{load}{effort}

(7.12)

Definition

Mechanical advantage

Machine jitna load overcome karti hai aur us par jitna effort lagaya jaata hai, unka ratio.

Example5 MA wala lever $100 N$ ke push se $500 N$ ka load utha deta hai.

1 se zyada MA ka matlab hai ki effort load se chhota hai. Iski keemat yeh hai ki effort ko zyada lambi distance tak chalna padta hai, isliye tumhara lagaya work load par kiye gaye work se kabhi kam nahi hota.

7.6.1 Pulley

Pulley (घिरनी) bas ek grooved wheel hai jo axle par aazaadi se ghoom sakta hai, aur uske groove mein rassi chalti hai. Gaon ke kuen par ek pulley opening ke upar ek beam se latki hoti hai: tum rassi ke ek end ko neeche kheenchte ho, aur doosre end se bandhi balti upar aati hai.

Fixed pulley tumhe lagne wala force kam nahi karti. $200 N$ ki balti uthane ke liye tum phir bhi lagbhag $200 N$ se kheenchte ho (friction ki wajah se thoda zyada), isliye uska mechanical advantage 1 hai. Yeh tumhe ek behtar direction deti hai. Neeche kheenchna upar uthane se aasaan aur safe hai, kyunki tum peeche jhuk kar apna weight use kar sakte ho (Fig. 7.12).

2/3Phir bhi $200 N,$ isliye MA = 1, lekin ab tum neeche kheenchte ho, aur tumhara apna weight madad karta hai.

Fig. 7.12Fixed pulley effort ki direction badalti hai; movable pulley uska size bhi kam karti hai.NCERT Figs. 7.24, 7.25 · p. 130

Teen scenes, har step mein ek. Pehle, ek insaan balcony se rassi par balti ko seedha upar kheenchta hai: 200 N ka upward effort arrow aur 200 N ka downward load arrow, label par likha hai: sirf haath (koi machine nahi). Doosre, ek beam se pulley wheel latka hai; rassi balti se uske upar se hokar zameen par khade insaan tak jaati hai jo neeche kheenchta hai: effort 200 N, load 200 N, MA = 1. Teesre, balti ek movable pulley se latki hai; rassi beam se neeche movable pulley ke around, phir upar fixed pulley ke upar se, aur neeche insaan tak jaati hai: effort 100 N, load 200 N, MA = 2, saath mein note ki do rassiyan load ko pakadti hain.

Quick check

2 mein se 1

Ek ideal single fixed pulley se

300 N

ka load uthaya jaata hai. Lagne wala effort lagbhag kitna hai?

300 N

150 N

100 N

600 N

Answer dekho

Answer (A) $300 N$

Fixed pulley sirf force ki direction badalti hai: effort = load, isliye MA = 1. Effort aadha karne ke liye movable pulley chahiye.

7.6.2 Inclined plane

Kisi dukaandaar ko tel ka bhaari drum truck par chadhate dekho. Woh use shayad hi kabhi seedha upar uthata hai. Woh truck se do takhte tika deta hai aur drum ko slope par push karke ya lurhaa kar upar chadhata hai. Is tarah use hone wali dhalaan wali surface ek inclined plane (आनत तल) hai. Slope asal mein kitni madad karta hai?

Activity 7.3NCERT Activity 7.3 · p. 131

Ramp par upar

Tumhe chahiye

free ghoomne wale pahiyon wala ek toy truck ya chhoti cart
ek spring balance
lagbhag 30 cm oonchi kitaabon ki dher
do smooth boards, lagbhag 60 cm aur 100 cm lambe

Pehle guess karo

Truck ko seedha upar uthane ke comparison mein, use lambe board par upar kheenchne mein lagega

zyada forcekam forceutna hi force

Spring balance ko truck se hook karo. Truck ko dheere aur steadily seedha kitaabon ke top tak uthao, aur reading note karo.
$60 c m$ wale board ko dher ke top se tika do. Balance ko board ke parallel rakhte hue truck ko board par dheere-dheere upar kheencho, aur reading note karo.
$100 c m$ wale board ke saath dohrao, jo kam dhalaan wala slope banata hai.
Har tarike ke liye force ko us distance se multiply karo jitna truck chala.

Table 7.5Seedha uthana vs slope par upar kheenchna

Tarika	Chali gayi distance (cm)	Force (N)	Force × distance
Seedha upar uthao	30
60 cm board	60
100 cm board	100

Tumhari entries apne aap save hoti hain.

DerivationInclined plane ka mechanical advantage

Weight $m g$ ke load ko length $L$ ke smooth inclined plane par steadily push karke height $h$ wale platform tak le jao (Fig. 7.13). Maano slope ke along lagaya gaya effort hai $F^{'} .$ Friction ignore karo, to tumhara kiya work load ko mili potential energy ke barabar hai:

F^{'} \times L = m g h

Isliye $F^{'} = m g h / L,$ aur mechanical advantage hai

MA = \frac{m g}{F^{'}} = \frac{L}{h}

(7.13)

Takhta hamesha us height se lamba hota hai jitna woh chadhta hai, isliye $L / h$ 1 se zyada hai aur effort load se kam hai. Same height tak jaane wala lamba, kam dhalaan wala ramp bada MA aur aur bhi chhota effort deta hai.

2/3MA = 2: $150 N$ , slope ke along $2 m .$

Fig. 7.13Lambe ramp par zyada lambi distance tak kam force lagta hai; work same rehta hai.NCERT Fig. 7.28 · p. 132

Right mein 1 m ooncha platform hai; ek label par load 300 N likha hai. Pehle step mein ek box platform ke bagal mein seedha upar uthaya jaata hai, upward force arrow ke saath, aur text mein likha hai F = 300 N, distance 1 m, F × d = 300 J. Doosre step mein 2 m ka takhta platform tak jaata hai, box us par hai aur slope ke along force arrow hai: F = 150 N, distance 2 m, F × d = 300 J. Teesre step mein lamba 3 m ka takhta kam dhalaan wala slope banata hai: F = 100 N, distance 3 m, F × d = 300 J.

Example 7.12NCERT Example 7.12 · p. 132

Dukaan mein ramp

Ek dukaan ke entrance par $25 c m$ ooncha step hai. Bhari handcart andar le jaane ke liye dukaandaar ek seedha ramp lagata hai jo step se $60 c m$ aage se shuru hota hai, zameen ke along naapa gaya. (a) Ramp kitna lamba hai? (b) Uska mechanical advantage kya hai? (c) Friction ignore karo, to $520 N$ ki handcart ko us par upar push karne ke liye ramp ke along kitna force chahiye?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Practice · 2 questions

Ruko aur socho: answers ke saath

Short answerMediumPause and Ponder Q9
Hill stations tak jaane wali ghat roads slope par seedha upar jaane ki jagah hairpin bends ke saath lambe zigzags mein chadhti hain. Inclined plane ke idea se samjhao ki aisa kyun hai.
Solution dikhao
Zigzag road ek lamba, kam dhalaan wala inclined plane hai. Same rise $h$ ke liye length $L$ kahin zyada hoti hai, isliye $L / h,$ yaani MA, bada hota hai aur gaadi ko chadhne ke liye kahin kam driving force chahiye. Woh zyada door chalti hai, lekin uska engine kam dhalaan ko sambhal leta hai, aur neeche aate waqt uske brakes use control kar sakte hain.
Short answerMediumPause and Ponder Q10
Ek worker chhat tak ya to seedhi khadi ladder chadh kar pahunch sakta hai, ya ek lambe dhalaan wale ramp par chal kar. Ramp aasaan kyun lagta hai, jabki potential energy mein gain same hai?
Solution dikhao
Dono tarah potential energy mein gain hai $m g h .$ Seedhi ladder par yeh poori energy chhoti si distance mein di jaati hai, yaani $h,$ isliye har kadam par worker ko poora body weight uthana padta hai. Ramp par wahi energy kahin lambi distance mein phail jaati hai, isliye har kadam par lagne wala force kam hota hai.

Quick check

3 mein se 1

3 m

lamba ek smooth takhta

0.6 m

oonche platform tak jaata hai. Uska mechanical advantage kya hai?

Answer dekho

Answer 5

MA = L / h = 3 / 0.6 = 5.

7.6.3 Lever

Activity 7.4NCERT Activity 7.4 · p. 133

Ruler jo uthata hai

Tumhe chahiye

ek 30 cm ka ruler
ek gol marker pen ya moti gol pencil
ek chhoti steel katori
ek mutthi ek jaise sikke

Pehle guess karo

Pen kahan rakhna chahiye taaki sabse kam sikke katori ko utha dein?

katori ke paasruler ke beech ke paassikkon ke paas

Ruler ko pen ke upar aise rakho ki pen ek end se $5 c m$ door ho. Katori us chhote end par rakho.
Doosre end par ek-ek karke sikke rakho jab tak katori uth na jaaye. Unhe gino.
Pen ko katori wale end se $8 c m$ aur phir $11 c m$ par le jao, aur har baar phir se gino.

Table 7.6Katori uthane ke liye lagne wale sikke

Pen ki jagah	Lagne wale sikke
katori wale end se 5 cm
katori wale end se 8 cm
katori wale end se 11 cm

Tumhari entries apne aap save hoti hain.

Tumhara ruler ek lever (उत्तोलक) tha: ek sakht bar jo kisi support par ghoomta hai. Ghoomne wala point fulcrum (आलंब) hai. Load bar ko ek jagah dabata hai aur tumhara effort doosri jagah, aur zaroori yeh hai ki har ek fulcrum se kitna door hai. In distances ko hum load arm aur effort arm kehte hain (Fig. 7.14).

Bar ko jhukao aur uske dono ends compare karo. Fig. 7.14 mein tumhara end badi distance $d_{1}$ tak neeche jaata hai, jabki load wala end dheere se sirf chhoti distance tak upar uthta hai: $d_{2} .$ Bar khud na energy store karta hai na banata hai, isliye (friction ignore karke) effort $F_{1}$ se tumhara lagaya work, force $F_{2}$ dwara load par kiye gaye work ke barabar hai:

F_{1} \times d_{1} = F_{2} \times d_{2}

(7.14)

Agar $d_{1}$ kai guna hai $d_{2},$ to load par push $F_{2}$ bhi kai guna hota hai tumhare effort ka, jo hai $F_{1} .$ Lever distance ke badle force deta hai: yeh tumhara lagne wala force kam karta hai, tumhara kiya work kabhi nahi.

1/2Fulcrum, load aur effort, load arm aur effort arm ke saath.

Fig. 7.14Lamba effort arm chhote effort se bada load uthwa deta hai.NCERT Fig. 7.32 · p. 133

Ek lambi iron rod apne left end ke paas ek triangular fulcrum par tiki hai. Chhote left end par ek bhaari sandook rakha hai jis par load likha hai, aur door right end par ek downward effort arrow lagta hai. Neeche dimension lines chhota load arm, load se fulcrum tak, aur lamba effort arm, fulcrum se effort tak, mark karti hain. Doosre step mein rod jhuk gayi hai: right end badi distance d1 neeche gaya hai aur sandook chhoti distance d2 upar utha hai, aur ek dashed outline dikhati hai ki rod pehle kahan thi.

Activity 7.5NCERT Activity 7.5 · p. 133

Metre-scale balance

Tumhe chahiye

ek metre scale (ya koi bhi lambi, halki, seedhi chhadi)
mazboot dhaaga
dhaage ke loops wale do ek jaise paper cups
lagbhag 15 ek jaise sikke ya metal washers
scale latkane ke liye ek hook ya stand

Pehle guess karo

Left mein beech se 40 cm par 3 sikke latke hain. Unhe balance karne ke liye right mein 6 sikkon wala cup kahan latkana chahiye?

beech se 40 cmbeech se 30 cmbeech se 20 cmbeech se 80 cm

Scale ke $50 c m$ mark par dhaaga kaskar baandho aur use aise latkao ki woh aazaadi se jhool sake. Agar woh level nahi latakta, to dhaage ko thoda khiskao jab tak level na ho jaaye. Yeh point fulcrum hai.
Har side par ek cup aise dhaage ke loop se latkao jo scale ke along khisak sake.
Left cup (effort) mein 3 sikke daalo aur use fulcrum se $40 c m$ par latkao. Use wahin rakho.
Right cup (load) mein 3, phir 4, phir 6, phir 8 sikke daalo. Har baar right cup ko tab tak khiskao jab tak scale level na ho jaaye, aur fulcrum se uski distance naapo.

Table 7.7Metre scale ko balance karna (effort: 40 cm par 3 sikke, 3 × 40 = 120)

Load sikke	Balance wali distance (cm)	Sikke × distance
3
4
6
8

Tumhari entries apne aap save hoti hain.

Balanced lever

\begin{aligned} effort \times effort arm \\ = load \times load arm \end{aligned}

(7.15)

Ise rearrange karne par lever ka mechanical advantage milta hai:

\begin{aligned} MA & = \frac{load}{effort} \\ = \frac{effort arm}{load arm} \end{aligned}

(7.16)

Lamba effort arm aur chhota load arm bada MA dete hain. Har machine ki tarah iski bhi keemat hai: tumhara end load se zyada door chalta hai, isliye tumhara kiya work kam nahi hota.

InteractiveMetre-scale balance

Ek metre scale apne beech se dhaage par latka hai, har side ek pan ke saath. Har pan ke liye plus aur minus buttons ek jaise sikkon ki ginti 1 se 8 tak set karte hain, aur ek slider fulcrum se uski distance 5 se 45 cm tak set karta hai. Beam us side jhukta hai jahan sikkon aur distance ka product bada ho, aur jab dono products barabar hon to level hota hai. Ek message dono products dikhata hai, aur jab load side par zyada sikkon ke saath beam balance hota hai, to mechanical advantage ko sikkon ke ratio aur distances ke ratio ke roop mein dikhata hai. New challenge button left pan ko fix kar deta hai aur tumse right pan ko balance wali position tak khiskane ko kehta hai.

Fig. 7.15Sikke daalo aur pans ko khiskao jab tak beam balance na ho jaaye, phir ek challenge try karo.

Example 7.13NCERT Example 7.13 · p. 134

Seesaw ko balance karna

Park ke ek seesaw ka fulcrum beech mein hai, aur har arm par fulcrum se $2 m$ tak har $0.5 m$ par seats hain. Meera ( $24 k g$ ) fulcrum se $1.5 m$ par baithi hai. (a) Use balance karne ke liye Kabir ( $36 k g$ ) ko doosri side kahan baithna chahiye? (b) Meera ka chhota bhai ( $12 k g$ ) uske saath uski seat par chadh jaata hai. Ab Kabir ko kahan jaana hoga?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Levers ki classes

Levers ko teen classes mein baanta jaata hai, is hisaab se ki beech mein kya hai: fulcrum, load ya effort. Fig. 7.16 aur Table 7.8 teeno dikhate hain.

1/3Fulcrum beech mein, jaise seesaw ya kainchi mein.

Fig. 7.16Beech mein kya hai, isse class tay hoti hai.NCERT Table 7.2 · p. 135

Wahi horizontal bar teen baar dikhaya gaya hai. Pehle step mein, Class I, fulcrum beech ke neeche hai, load left end par hai aur right end par downward effort arrow lagta hai; examples: seesaw, kainchi, crowbar. Doosre step mein, Class II, fulcrum left end par hai, load beech mein hai aur right end par upward effort arrow lagta hai; examples: wheelbarrow, nutcracker, bottle opener. Teesre step mein, Class III, fulcrum left end par hai, beech mein upward effort arrow lagta hai aur load right end par hai; examples: chimti (tweezers), chimta, jhaadu.

Table 7.8Levers ki classesNCERT Table 7.2 · p. 135

Class	Beech mein	Mechanical advantage	Examples
I	fulcrum	1 se zyada ya kam	seesaw, kainchi, crowbar, hand-pump ka handle
II	load	hamesha 1 se zyada	wheelbarrow, nutcracker, bottle opener
III	effort	hamesha 1 se kam	tweezers, fishing rod, tumhara forearm

Class III lever mein load se zyada effort lagta hai. Phir bhi yeh kaam ka hai, kyunki load wala end tumhare haath se zyada door aur zyada tez chalta hai: jhaadu ek bada arc ghoomti hai, aur tweezers se bareek control milta hai.

Roz ki machines ko dhyaan se dekho, to unke andar simple machines milengi: gaon ka hand pump apne piston ko lever se chalata hai, aur cycle ke brake handles bhi levers hain. Koi bhi machine energy ka source nahi hai. Zyada se zyada woh tumhara diya har joule aage pahuncha deti hai; asli machines hamesha kuch joules friction ki wajah se heat mein kho deti hain.

Practice · 3 questions

Ruko aur socho: answers ke saath

Short answerMediumPause and Ponder Q11
Lambe handle wala bottle opener bahut chhote handle wale opener se use karne mein aasaan kyun hota hai?
Solution dikhao
Opener ek lever hai. Uska tip cap ke upar tika hota hai (fulcrum), aur uska lip cap ke kinare ke neeche phansta hai (load), sirf lagbhag ek centimetre door. Lamba handle lamba effort arm deta hai jabki load arm same rehta hai, isliye MA (effort arm ÷ load arm) bada hota hai aur chhota push hi cap ko utha deta hai.
Short answerMediumPause and Ponder Q12
Ek maali pruning shears se moti tehni kaatte waqt use jaws mein gehra, pivot ke paas ghusata hai. Kyun?
Solution dikhao
Shears levers ka ek pair hain jinka fulcrum pivot hai. Tehni ko pivot ke paas rakhne se load arm chhota ho jaata hai jabki effort arm (handles) lamba rehta hai. MA bada ho jaata hai, isliye blades tehni ko maali ki pakad se kahin bade force se dabate hain.
Short answerHardPause and Ponder Q13
Ek online video mein jhoolte weights wala ek wheel dikhta hai jo hamesha apne aap ghoomta lagta hai aur bina battery, fuel ya push ke ek bulb bhi jala deta hai. Work aur energy ke ideas se samjhao ki aisi koi perpetual motion machine kyun kaam nahi kar sakti.
Solution dikhao
Axle par friction aur air resistance wheel par lagataar negative work karte hain aur uski mechanical energy ko heat mein badalte hain, aur bulb jalane mein bhi energy bahar jaati hai. In losses ki bharpaai ke liye koi energy nahi deta, aur energy banayi nahi ja sakti. Isliye wheel ki kinetic energy ghatti jaayegi jab tak woh ruk na jaaye. Jo machine hamesha chalti lagti hai, uska koi chhupa hua energy source zaroor hoga.

Quick check

4 mein se 1

Ek crowbar ka effort arm hai

1.2 m

aur load arm hai

0.15 m .

Uska mechanical advantage kya hai?

Answer dekho

Answer 8

MA = 1.2 / 0.15 = 8.

Real life meinNCERT Bridging Science and Society · p. 136

Gharat: girte paani se chalne wali chakki

Uttarakhand aur Himachal Pradesh ki pahaadiyon mein gaon ke log sadiyon se chhoti water mills mein anaaj peeste aaye hain, jinhe gharat ya panchakki kehte hain. Ek naali dhaara se paani lakdi ki ek khadi chute tak laati hai. Chute mein tezi se neeche aate hue paani ki potential energy kinetic energy ban jaati hai.

Paani ki dhaar mill house ke neeche ek horizontal wheel ke paddles se takraati hai aur use ghumati hai. Ek shaft is ghoomne ko seedha upar wale chakki ke paat tak le jaata hai, jo ek fixed neeche wale paat par ghoomta hai aur dono ke beech daala gaya anaaj peesta hai. Hydroelectric dams yahi chain bahut bade scale par use karte hain (Fig. 7.5), chakki ke paat ki jagah generator ke saath.

Aage ka safarNCERT The Journey Beyond · p. 139

Try karne ke liye cheezein

Rubber-band launcher. Ek rubber band ko do ungliyon ke beech ya ruler ke end par kheencho, mude hue kaagaz ki goli ko uske against peeche kheencho aur chhod do. 2, 4 aur 6 cm peeche kheencho aur har baar naapo ki goli kitni door udti hai. Kya koi pattern hai? (Sirf floor par rakhe target par nishana lagao, kabhi kisi insaan par nahi.)
Machine challenge. Ghar ke bekaar saamaan se ek aisa device design karo jo paani se bhari 1-litre ki bottle ko $20 c m$ upar uthaye, aur effort uske weight ke aadhe se zyada na ho. Spring balance se effort naapo aur jo mechanical advantage mila, woh calculate karo.
Online explore karo. PhET ke Energy Skate Park ya Pendulum Lab jaise free simulations mein mass, height aur friction badlo aur dekho ki energy bars kaise respond karte hain.

Recap

Summary aur key points

Koi force kisi object par work karta hai jab object force ke along move karta hai: $W = F \times s,$ jise joules mein naapte hain (Section 7.1).
Work zero hota hai agar koi displacement na ho, motion ke along koi force na ho, ya force motion ke right angle par ho (Section 7.1.1).
Work positive hota hai jab force aur displacement ek hi taraf point karein, aur negative jab woh opposite hon (Section 7.1.2).
Energy work karne ki capacity hai. Work–energy theorem: kisi object par kiya gaya work uski energy ke change ke barabar hota hai (Section 7.2).
Energy ke kai forms hain (mechanical, chemical, electrical, thermal, light, sound, nuclear), aur woh ek form se doosre form mein badalti hai (Section 7.3).
Kinetic energy motion ki energy hai, $K = \frac{1}{2} m v^{2}$ (Section 7.4.1).
Potential energy shape ya position se stored energy hai; Earth ke paas $U = m g h$ (Section 7.4.2).
Jab sirf gravity work karti hai, to mechanical energy $K + U$ conserve hoti hai; friction iska kuch hissa heat mein badal deta hai (Section 7.4.3).
Power work karne ki rate hai, $P = W / t,$ jise watts mein naapte hain, $1 W = 1 J / s$ (Section 7.5).
Simple machines force ka size ya direction badalti hain; mechanical advantage = load ÷ effort (Section 7.6).
Fixed pulley ka MA 1 hai, lekin isse tum neeche kheench sakte ho (Section 7.6.1); inclined plane ka MA $= L / h$ hai (Section 7.6.2).
Lever tab balance hota hai jab effort × effort arm = load × load arm, isliye uska MA = effort arm ÷ load arm (Section 7.6.3).
Koi bhi machine kul lagne wala work kam nahi karti, na hi energy banati hai.

Flash cards · 7

Formula cards

1 / 7

Apna NCERT exercise question dhoondo

Hamare practice questions ncert.ai ke liye likhe gaye hain aur NCERT exercises ko follow karte hain. Apni textbook ke question se match karne wala question dhoondo; uska answer uske saath hai.

Tumhari NCERT textbook mein	Yahan practice question
Pause and Ponder Q1	Ruko aur socho · Q1
Pause and Ponder Q2	Ruko aur socho · Q2
Pause and Ponder Q3	Ruko aur socho · Q3
Pause and Ponder Q4	Ruko aur socho · Q4
Pause and Ponder Q5	Ruko aur socho · Q5
Pause and Ponder Q6	Ruko aur socho · Q6
Pause and Ponder Q7	Ruko aur socho · Q7
Pause and Ponder Q8	Ruko aur socho · Q8
Pause and Ponder Q9	Ruko aur socho · Q9
Pause and Ponder Q10	Ruko aur socho · Q10
Pause and Ponder Q11	Ruko aur socho · Q11
Pause and Ponder Q12	Ruko aur socho · Q12
Pause and Ponder Q13	Ruko aur socho · Q13
NCERT Exercises Q1	Revise karo, socho, nikhaaro · Q1
NCERT Exercises Q2	Revise karo, socho, nikhaaro · Q2
NCERT Exercises Q3	Revise karo, socho, nikhaaro · Q3
NCERT Exercises Q4	Revise karo, socho, nikhaaro · Q4
NCERT Exercises Q5	Revise karo, socho, nikhaaro · Q5
NCERT Exercises Q6	Revise karo, socho, nikhaaro · Q6
NCERT Exercises Q7	Revise karo, socho, nikhaaro · Q7
NCERT Exercises Q8	Revise karo, socho, nikhaaro · Q8
NCERT Exercises Q9	Revise karo, socho, nikhaaro · Q9
NCERT Exercises Q10	Revise karo, socho, nikhaaro · Q10
NCERT Exercises Q11	Revise karo, socho, nikhaaro · Q11
NCERT Exercises Q12	Revise karo, socho, nikhaaro · Q12
NCERT Exercises Q13	Revise karo, socho, nikhaaro · Q13
NCERT Exercises Q14	Revise karo, socho, nikhaaro · Q14
NCERT Exercises Q15	Revise karo, socho, nikhaaro · Q15

Quick check: MCQs

7.1.2 Positive aur negative work4 questions
7.2 Work-Energy Theorem3 questions
7.3 Energy ke Forms2 questions
7.4.1 Kinetic energy3 questions
Gravitational potential energy3 questions
7.4.3 Mechanical energy ka conservation4 questions
7.5 Power3 questions
7.6.1 Pulley2 questions
7.6.2 Inclined plane3 questions
Levers ki classes4 questions

Glossary · 15

Key terms (English + Hindi)

energyऊर्जाoorja: Work karne ki capacity, joules mein naapi jaati hai.Chapter mein pehli baar yahan aaya →

fulcrumआलंबaalamb: Woh fixed point jiske around lever ghoomta hai.Chapter mein pehli baar yahan aaya →

inclined planeआनत तलaanat tal: Dhalaan wali surface jisse load ko kam force se, lekin zyada lambi distance mein, uthaya jaata hai.Chapter mein pehli baar yahan aaya →

jouleजूलjool: Work aur energy ki SI unit: woh work jo tab hota hai jab $1 N$ force kisi object ko apne along $1 m$ move kare.Chapter mein pehli baar yahan aaya →

kinetic energyगतिज ऊर्जाgatij oorja: Move karne ki wajah se object ke paas hone wali energy, $K = \frac{1}{2} m v^{2} .$ Chapter mein pehli baar yahan aaya →

leverउत्तोलकuttolak: Ek sakht bar jo ek fixed point, yaani fulcrum, ke around ghoomta hai.Chapter mein pehli baar yahan aaya →

mechanical advantageयांत्रिक लाभyaantrik laabh: Kisi machine ka load, effort se divide kiya hua.
mechanical energyयांत्रिक ऊर्जाyaantrik oorja: Object ki kinetic aur potential energy ka jod.Chapter mein pehli baar yahan aaya →

potential energyस्थितिज ऊर्जाsthitij oorja: Shape ya relative position ki wajah se stored energy; Earth ke paas $U = m g h .$ Chapter mein pehli baar yahan aaya →
powerशक्तिshakti: Work karne ki rate, $P = W / t .$ Chapter mein pehli baar yahan aaya →
pulleyघिरनीghirni: Groove wala wheel jo rassi ko guide karta hai; fixed pulley effort ki direction badalti hai.Chapter mein pehli baar yahan aaya →

simple machineसरल मशीनsaral masheen: Pulley, ramp ya lever jaisa device jo force ka size ya direction badal kar kaam aasaan banata hai.Chapter mein pehli baar yahan aaya →

wattवाटvaat: Power ki SI unit: ek joule per second.Chapter mein pehli baar yahan aaya →
workकार्यkaarya: Force dwara kiya jaata hai jab jis object par woh lagta hai, woh force ke along move kare; constant force ke liye $W = F \times s .$ Chapter mein pehli baar yahan aaya →
work-energy theoremकार्य-ऊर्जा प्रमेयkaarya-oorja pramey: Kisi object par kiya gaya work uski energy ke change ke barabar hota hai.

Work, Energy, and Simple Machines: Class 9 Science Chapter 7 Hinglish mein

Is chapter mein aap kya seekhenge

7.1 Constant Force se kiya gaya Work

7.1.1 Kiya gaya work kab zero hota hai?

7.1.2 Positive aur negative work

Ruko aur socho: answers ke saath

7.2 Work-Energy Theorem

Ruko aur socho: answers ke saath

7.3 Energy ke Forms

7.4 Mechanical Energy

7.4.1 Kinetic energy

Ruko aur socho: answers ke saath

7.4.2 Potential energy

Gravitational potential energy

Ruko aur socho: answers ke saath

7.4.3 Mechanical energy ka conservation

Ruko aur socho: answers ke saath

7.5 Power

7.6 Simple Machines

7.6.1 Pulley

7.6.2 Inclined plane

Ruko aur socho: answers ke saath

7.6.3 Lever

Levers ki classes

Ruko aur socho: answers ke saath

Summary aur key points

Practice questions answers ke saath (NCERT “Revise karo, socho, nikhaaro”)

Apna NCERT exercise question dhoondo

Quick check: MCQs

Key terms (English + Hindi)

Tum chapter ke end tak pahunch gaye