State Archimedes principle
Scenario
Ek tub paani se poora bhara hai, jab aap usme jaake baithte hain to thoda paani bahar gir jata hai.
Kya ye gira hua paani aapko bata sakta hai ki aap par kitna upthrust (buoyancy) lag raha hai?
Mental model
Jitna liquid tumne hataya (displace kiya), utna hi liquid ka wajan tumhe upar dhakel raha hai.
Jab koi body kisi fluid mein dubti hai, toh woh kuch fluid ko apni jagah se hata deti hai (displace). Hataye gaye fluid ka weight exact barabar hota hai uss upthrust ke jo fluid object par lagata hai. Yahi Archimedes' principle hai.
Explanation
Archimedes' Principle buoyant force ko calculate karne ka exact mathematical tarika batata hai. Law kehta hai: 'When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.'
Iska matlab hai ki agar ek object paani mein daalne par `2 kg` (mass) paani bahar chalak deta hai ya displace kar deta hai, toh us object par lagne wala buoyant force uss `2 kg` paani ke weight ke barabar hoga. (Yani `2 kg * 9.8 m/s^2 = 19.6 N` ka upward force).
Yeh principle sirf paani par nahi balki hawa (gases) par bhi lagta hai. Lactometers (jo doodh ki purity check karte hain) aur hydrometers (jo liquids ki density napte hain) dono Archimedes' principle par base hote hain. Submarines aur ships ki designing mein ye principle sabse zyada kaam aata hai kyu ki unko itna paani displace karna hota hai ki wo doobe na.
Worked example
Problem: An object displaces `500 N` of water when fully immersed. What is the buoyant force acting on it?
- Archimedes' principle seedha kehta hai ki upthrust displaced water ke weight ke barabar hota hai.
- Weight of displaced fluid diya gaya hai (`500 N`), toh buoyant force bhi wahi hoga.
Answer: `500 N`
Problem: A metal cube is submerged in alcohol. It displaces `2 kg` of alcohol. What is the upthrust on the cube? (Take `g = 9.8 m/s^2`)
- Pehle hataye gaye (displaced) alcohol ka wajan nikalna padega, kyu ki yahan mass diya hai (`2 kg`).
- Archimedes ke mutabiq, yahi weight upthrust hai.
Answer: `19.6 N`
Key points
- Buoyant Force = Weight of Displaced Fluid: Upthrust hamesha hataye hue liquid ke barabar hoga. Agar zyada liquid hataya, to upthrust zyada.
- Applies to All Fluids: The principle applies equally to both gases and liquids.
Common mistakes
- Confusing mass of displaced fluid with weight: Log puchte hai, upthrust kya hai aur jawab mein mass (`kg`) bata dete hain. Upthrust force (`N`) hai, isliye mass ko gravity se multiply karna zaroori hai.
Recall questions
- What is the relationship between upthrust and the weight of displaced liquid?
- What is Archimedes' Principle?
- What is the upward force called?
Questions & answers
State Archimedes' principle.
When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.
Approach: Write the exact statement mentioning 'fully or partially', 'fluid', and 'weight of fluid displaced'.
How do submarines use Archimedes' principle to dive?
By filling their ballast tanks with water to increase their average density.
Approach: Explain that when weight exceeds the buoyant force of displaced water, the submarine dives.
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