39I challenge you to prove that this is within the bounds of the JEE syllabus.
Thank you.
in calculating curved area and volume of a cone .
let height =h and radius of base = r , where tanθ = r/h
now my doubt is :
suppose vertex of cone is origin and height is along x axis
then we can write curved area = ∫2πy (1 + (dy/dx)2)1/2 dx
but for volume we write
V = ∫πy2dx
what is wrong in writing volume = ∫πy2(1 + (dy/dx)2)1/2 dx
isnt this more correct ?
if no,
then why is the area not equal to ∫2πydx
in calculating volume we are making an approximation for calculating volume of the differential disc ,but by integrating , we will be summing up the error wich will become quite big isnt it ??
if u argue that we take volume as Σ lim dx→0 and hence error is accounted , then why cant we use same arguement and write area = ∫2πydx
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14 Answers
39
1Dude, its not necessary that you get answer to every question of yours on this forum. Try posting in on other sites. Its good that you are doing something beyond JEE syllabus, but it won't help you in JEE.
1pritish why do u think this is out of syllabus i dont get it
it is just simple calculus
GUYS THIS IS WITHIN JEE SYLLABUS AND A QUESTION IN PHYSICS ABOUT SIMILAR CONCEPT HAS COME ALSO ( IT NEEDED US TO CACLULATE THE VOLUME OF A PARABOLOID )
and this type of derivation is almost everywhere, it is in waves , in fluids ,etc
exampple in calculating PE stored in a stretched string thru wich a wave is propogating we write
Work done =∫ FdL
where dL = (dy2 + dx2 )1/2= (1+ (dydx)2)1/2dx
this work done is stored as PE
now tell me howe can u say it cannot come in jee, we are using same concept somewhere else in other chapters and u guys say it is not in syllabus
IIT paper setters use this opportunity and put question on such concepts wich many people think isnt in syllabus but is actually well within syllabus
let me giv u one more example
in conics syallbus it is clearly mentioned conics with standard eqn
but we will hav to study general equations also because they have many times asked question on conics' general eqn in other chapters
49quote::
EmInEm said: "GUYS THIS IS WITHIN JEE SYLLABUS AND A QUESTION IN PHYSICS ABOUT SIMILAR CONCEPT HAS COME ALSO ( IT NEEDED US TO CACLULATE THE VOLUME OF A PARABOLOID ) "
Please show me the question...!!
1why is every one out here wanting to prove this one to be out of syllabus ....
i am not saying that this is out of syllabus but many other posts even of mentors here are way out of syllabus ( like using cauchy schwarz inequality , jensons inequality ,etc etc )
if any can help me i will be greatful
btw please dont avoid this thread, i feel some mentors here are purposely arent answering even when they know wat the concept is
sirs please help it will take just a minute to answer
1btw shubomoy i dont remember exactly the question but it was like :
a cylindrical tank ( with dimensions given ) contains some given amt of water . the tank is rotated with omega, abt an axis _|_ to cylinder's cross sectional area, then find the radius of the circular area untouched by water while it is rotating
1A general word of advice to all JEE takers,
Its important to stick to the subscribed syllabus, but having said that,
please do not restrict your selves to mere limits set by someone. Expand your horizon,
don't cramp your creativity.
49EmInEm..physics was never maths dependent..
maths is just a support to physics..
i just wanted to see the question in which we had to apply such a dangernak integration and that too in JEE..:P
well..i do not know (neither do i care much) if the sum u have given is in JEE sylabi but what i know is surely the sum u have given can be done easily without dangernak math solving (dude i am bad at maths and so try to avoid rigourous mathematical approaches to physics problems)
as of ur integration i m now ultimately giving it a look ... just out of curiosity what was it that created so much unrest! :P
49sorry..abhi time nahi bacha..seems an interesting sum! :but i am bad at maths! :D
bye!
1nothing depends on maths ever to exist, but everything in this universe requires mathematics to understand abt it
1subhomoy why dont u just give me the answer rather than wasting even your own time by writing something irrelevant
