Determine if displacement is zero
Scenario
Aapne ground ke bohot saare round lagaye paseena bahaya, aur wapas usi bench par baith gaye jahan se bhaagna shuru kiya tha.
Kya physically aapne koi displacement ki agar aap ghumm kar wapas wahin aa gaye?
Mental model
Displacement is purely 'Start Point = End Point? If yes, then zero.'
Displacement beech ke safar ko ignore karke sirf do cheezein check karta hai: safar kahan se shuru hua aur kahan khatam. Agar ye dono points exactly ek hi jagah par hain, toh seedhi line ban hi nahi sakti, isliye displacement 0 hota hai.
Explanation
Physics mein kayi aise situations aate hain jahan object bahut tezi se lamba distance cover karta hai, par end mein uski displacement zero ho jati hai. Yeh determine karne ka sabse simple rule yeh hai: hamesha initial position aur final position ko ek sath compare karo.
Agar object ka starting point aur uska aakhiri point space mein exactly same point par overlap karte hain, toh inke beech ka shortest distance naturally zero ban jayega. Jaise ek circular running track par jab koi phera (lap) lagata hai, to ek round pura hone par woh jahan se bhaga tha wahin pahunch jata hai.
Same logic applies agar ek pendulum jhool kar wapas apni mean position par aaye, ya ek pathar hawa mein phenk kar wapas aapke haath mein aa gire. Yahan par raste ki shape chahe circular ho, straight-line (U-turn) ho, ya koi aur complex pattern ho, displacement ki value zero hi aayegi.
Yeh concept graphical representation mein bhi bahut madad karta hai. Agar kisi velocity-time graph ka x-axis ke upar wala area (positive displacement) uske x-axis ke neeche wale area (negative displacement) ke exactly barabar ho, tab bhi net displacement zero hota hai. Is concept par objective questions aksar board exams mein test kiye jaate hain.
Worked example
Problem: A swimmer dives into a 50m long pool, swims to the opposite end, and then swims back to the starting point. Is his displacement zero?
- Initial point diving point hai. Swimmer wapas tair kar aakhiri mein wahin diving point par aa jata hai.
- Kyunki shuruati aur aakhiri point same hai, inke beech ka shortest distance zero hai.
Answer: Yes, displacement is zero.
Problem: A car moves 10 km East, then 5 km West, then again 5 km West. What is its displacement?
- Pehle car 10 km positive (East) direction mein jati hai.
- Phir car 5 km opposite (West) direction mein jati hai. Phir se 5 km aur West mein jati hai.
- Total dekhein toh wapas 0 (starting point) par aa gayi.
Answer: 0 km
Key points
- Same initial and final position: If an object returns exactly to its starting point, its displacement is automatically zero.
- Closed loops: Moving in complete circles, U-turns back to the start, or any closed-loop path results in zero displacement.
Common mistakes
- Confusing zero displacement with zero distance: Students aksar displacement zero dekh kar sochte hain ki body move hi nahi kari (object at rest). Par aisi body ka distance bahut high ho sakta hai.
- Assuming half a circle is zero displacement: Kai baar bache aade (half) round me bhi displacement zero kar dete hain. Zero tabhi hoga jab round 100% complete ho.
Recall questions
- Under what single condition is displacement strictly zero?
- If a body covers half a circular track, is its displacement zero?
- Can a moving object have zero distance and non-zero displacement?
Questions & answers
An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.
Yes. A student going to school from home and coming back home. Distance is not zero, but displacement is zero.
Approach: Any example of a closed loop or round trip proves the point.
A particle moves in a circle of radius R. What will be its displacement at the end of a full revolution?
Zero.
Approach: After a full revolution, the particle is exactly back where it started, so the straight line distance between start and end is zero.
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