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REspected hdani,
Plzzzzzzzzzzzzzzzzzzzzzzzzzzz post the links for Schaum series.. PLzzzzzzzzzzz I really want them.. Its one of the best books by TMH and they are quite useful for preparation of IIT JEE.. especially the one on physics.. I have seen some of the ques. in IIT directly picked up from there..
I would be so grateful to you that i dont even have words to espress.. But one request dont post the books on the current server.. I am not able to download from it.. Would you be kind enough to post on some other server..
With regards,
Prakhyat
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Hii Prashant,
First of all colud you please mention the book you are reffereing from, it will be more easier for me.. Next thing there is no doubt about friction it has to be there for pure rolling and i think you understand that.. Moreover i feel the author of the book wants to understand that by yourself just by taking into the account that it is pure rolling.. Regarding F well if you are talking about the force being applied it
applied cannot get cancelled in any case because it is the cause of entire motion and if you are taking about Fs not being mentioned in the solutuon then it must have been wriiten in a different form.. I hope you get that..
And this is for abhiman
Plzz check your answer it seems to me that your solution is not correct.. I think you commited a silly mistake and that is for newtons law for the plank is :
F-fr = M1AP => AP = (F- fr)/ M1 wheras you have taken AP to be F- fr/M1
Just check your solution.. I hope you'll agree with me..
If still than ne thoughts just feel free to ask..
With regards,
Prakhyat
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Hii Prashant,
Well I dont noe how to provide with your diagrams but I will try and explain the secnario and then solve it...
Now first of all i think you have missed metioning about the friction between the plank and sphere.. Because unless and until there is friction it is not possible for sphere to roll without slipping.. Therefore i am assuming there is friction between plank and sphere and that is - u (mu).. [Dude sorry i am not able to use the symbols provided so sorry for ne inconvience in understanding the solution]
Let the acceleration of plank be 'A' and that of CM of sphere be 'a'.. When the plank will pulled with a force F say towards rightwards then static friction Fs would start acting on the plank in the backward direction and it equal and oppostie force on the sphere in foward direction which would provide the sphere with an angular acceleration alpha in the opposite direction...
Now first writing the equations for cylinder:
Torque in CM's frame = ICMalpha
Now as there is only one force that of static friction Fs providing torque to the sphere the above equatio will become:
FsR = 2/5 M2R2 alpha where R= radius of sphere, M2 = Mass of sphere and
2/5 M2R2 is moment of inertia about CM..
The above equation reduces to: Fs = 2/5 M2 (R alpha) ----------------- (1)
Now for the plank:
aCM,Plank = aCM - aplank
=> - (R alpha) = a - A or A - a = R alpha ............ (2)
Also, for sphere from Newtons Law, Fs = M2.aCM = M2a.............(3)
and for the plank F - Fs = M1A ............ (4)
and now solving 1, 2 , 3 ,4 we can get the answer..
I hope i have been able to explain the solution... If any problems then feel free to ask...
With regards
Prakhyat
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Hiii Manisha
In case of a simple harmonic motion:
K.E. = 1/2 mw2(A2-y2)
P.E. = 1/2 mw2y2
M.E = K.E + U = 1/2 mw2A2
( where w stands for omega)
Now y=A/2 given, therefore
Fraction of KE = fK = K.E./ M.E. = 1-(y2/A2) = 1- 1/4 = 3/4
Fraction of PE = fP = P.E / M.E. = y2/A2 = 1/4
With regards
Prakhyat
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Hi Abhiman,
Well i wont go in too much details and try to make it as simple as i can(Plz note i am only talking about 1-D conservative field) Also in the entire discuusion i would be assuming you know a bit of calculus. :
Let the potential energy of a system U be a function of x i.e U=f(x) where x is the displacement of the particle along the x axis. And we know that F= -dU/dx..
Now a plot a graph between U and x... When F will be zero then U has only three possibilites(from the knowlegde of Calculus) i.e either U can obtain a maximum (when d2U/dx2 is negative) or a minimum (when d2U/dx2 is positive) or constant (when d2u/dx2 is zero)
When U = mininum => d2U/dx2 > 0, equllibrium is stable
U = maximun => d2U/dx2 < 0 , equllibrium is unstable
and U = Constant => d2U/dx2 = 0, equllibrium is neutral
Let me take an example and explain it with you with an example:
Suppose the potential energy of a system is given by the function: U=ax2- bx (u can plot the graph by your self) where a and b are postivie constants. You have to find out a) equilibrium position and b) whether the system is satble or unstable.
Now see Force= F = -dU/dx
So for part a) differentiate the given function with respect to x i.e
F= -dU/dx = -d(ax2-bx)/dx = b- 2ax
And for equllibirium F=0 => b-2ax=0 or x = b/2a
In the second part of stabilty calculate d2U/dx2 i.e
d2u/dx2 = d(dU/dx)/dx = d(2ax-b)/dx = 2a which is positive therfore U is minimum and it is a stable system
I hope i have explained what you wanted to know. If any queries feel free to ask
With regards,
Prakhyat
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Dear Vaibhav,
I absolutely agree with Puneet.. Studying in a good institute wont make you get into an IIT.. It your hard work which will lead you there.. They say that 95% of the hard work is your own and only 5% of teachers.. I would say study heard for the months of Jan. and Feb.. Pick up good books and get your basic fundametal concepts clear.. And then try to solve numericals.. Then decide for your self whether it is sufficent or not.. And for your knowlegde i noe people who didnt go to any tutions and still got gud ranks.. I think that would solve your problem.. If any querys than feel free to ask..
With regards,
Prakhyat
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Respected Puneet,
I in no way wanted to offend you... And i absolutely agree with you that different individuals have different view about preparation....
Sir you are at higher level than myself as being already going through all the process and vastly more experienced... But the point i was trying to make that what i have noticed on this forum is that most of you experts advice books from ARIHANT... which not only in my personal view but also from the view of my teachers, and IIT slections for the year 2006 (AIR 1,4,6,7,25,61).
I am not at all trying to prove a point that what i am saying is absolutely correct.. I may be even wrong... What basically i am trying to say is that for someone who has just sarted +1 books such as Freedman, Fay are of great help...
They say that for cracking the paper of IIT you need to have your concepts clear which i think do become clear after reading the theoritical books...
I felt that doing these books along with your coaching material would make your concepts clear... And then you make those concepts clear by solving as much questions as you can..
I in no way feel what i am saying is correct and would like you to correct me if you feel i am wrong... Your views are very of great importance and valuble, so would be looking forward to your reply...
With regards,
Prakhyat.
P.S.- Other experts plzz feel free to express your views.. This discussion is quite important ant i would like to hear from everyone of you.
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Repected Puneet,
I completely disagree with you regarding books to be read for Maths.. Arihant publishers have books which are good but the questions provided in the books are not pertaining to IIT..
Regarding books here is what i think one should read :
MATHS
1) Higher Algebra - Hall & Knight
2) Trignometry - S L Loney
3) Coordinate Geometry - S L Loney
4) Calculus - Thommas & Finney
5) IIT-JEE Maths- TMH
PHYSICS
1) Universtiy Physics ( Freedman and Young) - This book is required to clear the concepts.
2) Concepts in Physics I & II (H.C. Verma)
3) General Problem in Physics (I.E. IRODOV)
CHEMISTRY
Physical Chemistry
1) Problems in Chemistry - R.C. Mukherjee
2) Macmurry Fay
Organic Chemistry
1) Organic Chemistry - Solomon
Inorganic Chemistry
1) Concepts of Inorganic Chemistry - J.D. LEE
2) Inorganic Chemistry - O.P. Tandon
Apart from all the above mentioned books NCERT books are a must..
I guess i have metioned all the books that i noe and which are good enough for anyone to get in to IIT..
With regards,
Prakhyat
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Hiii
IIT doesnt mention netwons law directly but as it is related with lenses it can be regarded to be in the syllabus.. Doin it will not do any harm... And in my personal opinion it is not a big deal even if you do it.. Its derivation is quite simple.. Still a direct question related to Newtons Law is a far possibilty...
I hope admin would agree with me.. If incase i am wrong then do tell me..
With regards,
Prakhyat
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Hiii
Though the question seems incomplete still i can provide you with the answer in genreal terms..
Apparent depth of liquid = h = [n2Hcos3 a ] / [n2 - sin2a]3/2
where n = refractive index of liquid
H = Height of tank
a = Angle made by the line of sight of man with vertical i.e 90 - angle made by the line of sight with horizontal
The above answer holds for any gneral angle 'a'. But if a< 5 then the apparent height of liquid simply becomes H/n.
Now just put in the values and you'll get your answer..
Regarding the solution its quite difficult to post because it is exhaustive, which is derived using a figure and i wont be able to explain it withought the figure.. Admin plzz help me out with that so i am also able to post the solution..
With regards,
Prakhyat
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