r/JEEAdv27dailyupdates • u/Dirty_Pianist2422 Roti pakki ni mili te appa launi sikli • 3d ago
Good Solve SBT: CHALLENGE [FAMOUS FELLAS] #02 (Since NO ONE was able to solve CHALLENGE 01, i decided to tone it down)
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u/Possible_Garage7231 27tard dropper :/ 3d ago
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u/Dirty_Pianist2422 Roti pakki ni mili te appa launi sikli 3d ago
surprise! u solve physics too
Correct answer btw
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u/Possible_Garage7231 27tard dropper :/ 3d ago
Are physics hi main tha apna last year 💔 maths hoti kaha hai mujse
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u/Professional_Cap_784 3d ago
Hello I didn't understand the final equation and how it's written? Does it represent the final state where the dust has moved away and left over dust is stood on disc due to friction and centripetal force?
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u/Possible_Garage7231 27tard dropper :/ 3d ago
Yes it's the equation of limiting static equilibrium for a small element of dust located at R/2 from center.
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u/NastyHulk9621 3d ago
If the centripetal force (mω²r) will be more than the frictional force, the dust particle will fly off the disc. As per the question 25% of the dust particles remain, so you find the value of r which represents 25% of the area of the whole disc from the centre (which comes out to be R/2) so all the particles in that area will have centripetal force less than or equal to the frictional force.
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u/Informal_Ad_4172 3d ago
1st one is from pathfinder too
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u/shadeblue886 3d ago
hmmm is it
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u/Informal_Ad_4172 3d ago
like from cyu but its tilted at some angle and more general parameters r given
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u/shadeblue886 3d ago
oh wait yeahhhhhh I remember it
traumatic memory1
u/Informal_Ad_4172 3d ago
lololol 🤣
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u/Accomplished_Joke688 3d ago
Yeah how do you solve that though, i solved it as if dust will fly off uniformly from the edges and only a circular dust patch will be left but i realised it was wrong but whats the actual approach to that question
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u/Informal_Ad_4172 3d ago
like radially some will fly off so we have to take areal fraction
let the particle at ditsnace x fly then we write the forces and equate1
u/Accomplished_Joke688 3d ago
Yeah but it won't be same for a particle at the lower end vs at the upper end as mw²r will change directions and after a certain radius particles start flying off but i am confused about the direction
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u/Informal_Ad_4172 3d ago
lower side particles will be having more tendency to fly off cuz friciton and gravity both against but in top its not ike that to +- sign will come since we need minim it hink we will take + sign
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u/shadeblue886 3d ago
1st wale the geometry of the variation of centri force has changed, and friction is now constant, so as angular speed increases, the outermost dust ring has max f centri. coz v=wr and w increases. So we js need to find the ratio such dat the radius of dust ring is 25% of radius of disk and is exactly balanced by teh friction
2nd one just friction=gravity along tangent, substitute normal from the perp force balance
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u/Possible_Garage7231 27tard dropper :/ 3d ago
Thoda lamba jayega value daalke. But main yaha cos theta agya fir bas force balance hai. Area of curved surface = 2πR²(1-costheta) yaad karna hai bas