JEE_Mains 2014:: Physics : Ambiguous Problem

In JEE_Mains 2014 , CBSE asked an problem which doesn't have any correct alternative . And Most surprising thing is tat they Did not give bonus marks to that problem!

So Do you know what is reason behind this ? Is they used some approximation ? If so then what was that ? How we can calculate that approximation !

Problem:: Q-28FittJEE

Answer::(Given by CBSE ) JEE_mains have finally said that answer is Option -3 i.e ${ R }^{ 2 }\sqrt { \cfrac { { \rho }_{ w }g }{ 3T } }$ . is correct . They did not give Bonous marks.

Expected Solution:: Since no data of bubble is given , So we simply Used that at this time , just before detachment, Surface tension force should balanced buoyant force: $\displaystyle{(2\pi rT)\sin { \theta } =\left( \cfrac { 4\pi { R }^{ 3 } }{ 3 } -\cfrac { 2\pi { r }^{ 3 } }{ 3 } \right) { \rho }_{ w }g\\ 2\pi rT\times \cfrac { r }{ R } \approx \cfrac { 4\pi { R }^{ 3 } }{ 3 } \times { \rho }_{ w }g\\ \boxed { r\approx { R }^{ 2 }\sqrt { \cfrac { 2{ \rho }_{ w }g }{ 3T } } } }$

Recently I gave JEE_Mains 2014 paper at home for Practice , and this question Baffles me again !

Please This is open discussion , So Please tell how they approximate answer as option-C ? And what are other different approaches to this Problem ? Please share everything you know about this problem ! Even My teachers says that some-one of CBSE used some approximate and just brute force method to proove this approxiation , Really I want to know about such approximations if it exist !

Thanks!

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Comments

This problem is wrong. It cannot be solved by brute force method. It cannot be solved by any method. We need to know the pressure at bottom of liquid. We can use buoyant force concept if and only if an object is totally surrounded by the fluid. In this case, due to the flat part at the bottom, we have to calculate upward force differently. And to do this, we need the pressure at bottom of liquid.

If any one gets the answer using believable approximations, please share them.

@Deepanshu Gupta @Shashwat Shukla @Mvs Saketh

Raghav Vaidyanathan - 6 years, 3 months ago

That is not a problem bro, No ,real object is ever so attached to bottom that not a single layer of water is beneath it to push it up, just like in optics, no glass slab (example paper weight) is so firmly held to ground without a layer of air beneath it that light can enter from bottom in any angle (it can enter at maximum critical angle) ,

Also, that is why we neglect Air pressure when we calculate weights of real life object, because there is always a layer of air below it and hence net pressure becomes the same as buoyant force hPg, and since for air P is very low(not very dense) , we neglect it, but other wise Air pressure would have a significant effect as it is $10^{5}$ pascals.

similarly, here it is not very unreasonable to say that there is some water layer at the bottom which we cannot see which pushes it up and net result is buoyant force

Mvs Saketh - 6 years, 3 months ago

No, there is no layer in the bottom. I understood all that you said, and I have thought about all these things before. Yes, you are right about the $10^5$ thing, that is why it is difficult to remove those suction cup type thing.

Now think, In this case, the bubble is formed in bottom of vessel. It is said to be attached to it. This means that the boundary of the flat part is physically connected to the vessel, hence creating a boundary between the air inside the bubble and the water outside it. You can also think of it this way: if there is a layer of water(however small) below the bubble, this means that the bubble is fully formed, and thus there is no question of it staying at the bottom, it will immediately rise!

@Raghav Vaidyanathan – Working under the approximation $r<<R$ means that the volume of the bubble that is 'missing' is very small and thus the net force acting on it by the water is approximately equal to the buoyant force. We don't need to know the pressure.

@Raghav Vaidyanathan

Shashwat Shukla - 6 years, 3 months ago

@Shashwat Shukla – Yes, I wanted to say the same thing.

Ronak Agarwal - 6 years, 3 months ago

@Shashwat Shukla – Yes, assuming that approximation seems to get us to the answer that the author has posted. Which is not the correct one(according to CBSE).

@Raghav Vaidyanathan – So you're trying to get the answer posted by CBSE and in doing so you're trying to work without any approximations...right? If so, then I agree that pressure at the bottom needs to be specified.

There is a way to get the answer however. But I don't feel it is justified. It is a matter of definition(and subsequent analysis based strictly on the definition).

It looks like what they mean by a bubble is a surface with two sides. It often happens that CBSE goes with definitions and $if$ you $define$ a bubble as an object that has two layers , so as to differentiate it from a drop which has only one layer,

Then the LHS becomes $(4\pi rT)sin\theta$ and we get option C.

@Shashwat Shukla – Yeah, I thought we might be able to understand what they did if we considered the actual case and then go about doing approximations. And yes, your explanation for the missing factor of $2$ is plausible. They might have done the same.

@Shashwat Shukla – Sorry I was not available for discussion , Since Electricity is gone in my house ! But okay I'am contuning now::

Yes May be if we just want to match the option-c , then may be you are correct , May be Possible they unnesseseerily assume bubble has two layers!Yes which can't be stable when we are heating , is they ? But what about If we Just want to do this question from very basic ? I mean by doing some calculation of Pressure at the circular bottom ? or Can we do by using Ideal behaviour of air inside bubble ? @Shashwat Shukla @Mvs Saketh @Ronak Agarwal @Raghav Vaidyanathan

Deepanshu Gupta - 6 years, 3 months ago

@Raghav Vaidyanathan – definitely i agree with you on that,if there was a layer of water, there was no scope for surface tension to hold it to the bottom,

I too doubt it now, you are right, the only logical way to solve this would be to deal with the air inside the bubble and find its pressure,

@Ronak Agarwal help?

@Mvs Saketh – Well, as far as I remember, bonus marks were given for this question later. (After corrections)

Pranjal Jain - 6 years, 3 months ago

@Pranjal Jain – No , I know Because I give that exam , and I did not get marks! See Set E Question Paper Q-28 physics

See This official answer

It looks like what they mean by a bubble is a surface with two sides.

But this is definitely incorrect reasoning and the question is wrong, I guess.

ahh , But bro can you please explain what is mechanism of This Bubble formation ? I don't think that two layers will form on heating ? Please discuss

Agreed. I also don't think two layers are formed and that's why I said that this logic is wrong.

But the thing is, it often happens that CBSE goes with definitions and $if$ you $define$ a bubble as an object that has two layers , so as to differentiate it from a drop which has only one layer, then maybe they expected us to go by this definition of a bubble.

@Sudeep Salgia @Karthik Kannan @jatin yadav will you guys please put some light on it ? And all other freinds Please Discuss this ! Thanks!

This question is wrong, it is given in FIITJEE to be wrong as well, i have seen it before i thought marks were given for that . and no approximation can justify that

No No , actually CBSE doesn't Give Bonous , That's why I'am Posting It ! I just want to know why they did not bonous it ? And If they did not Bonous It , then Possible that may be do some brute force method to justify this option , Since It is Single correct! Yes I Know It is wrong ! but why , they did not bonous it ? Since It is prestigious exam in India , So If this question is completly wrong then , It should be given Bonous Marks ! Since It may be question carear !

And My Sir Say's they brutly Proved it that by some approximationS , I know they are wrong , but due to their prestige they unnecesserry proved that ! I don't know how , Even It is difficult for me to digest !

How much you got in your practice paper, well Jatin Yadav and others discussed this question previous on brilliant and they expected this question to be given as bonus, but as you are saying they didn't.

In my view they should give it as bonus.

@Ronak Agarwal – well I got total of 322 , and I got 101 in physics and 110 in maths and 111 in chemistry ! I did too many mistakes in physics! what about you how did you got when you give at home ?

And Yes I agree that they should give , but unfortunately they didn't!

@Deepanshu Gupta – I got 320 in mains, chemistry took me down , Physics-110,Maths-115,Chemistry-95

@Deepanshu Gupta – You already gave JEE-Mains 2014, so why did you give it again , also you got 322 in mains you gave previous year no.

@Ronak Agarwal – Actually I'am practising all JEEMains Paper , to find which topics I need to be practise and revise , Since It is impossible to give revise whole course ! And Actualy i did not give only this year paper , I give 2013 and all 4 of online 2013 paper too ! And Now I gave 2014mains and , my next target is to give all 4 Mains 2014 Online Papers.

So It is just for finding what topics are need to be revise ! that's why I gave that , also I want to anaylise my Last year mistakes So I gave it.

@Deepanshu Gupta – So the marks you posted were the marks you got when you actually gave JEE Mains Last Year.

@Ronak Agarwal – No, no I got worst marks in last year, that was horrible experience! And this marks was got a day before when I gave it again at home !

@Deepanshu Gupta – The same accuracy problem pestures me also, most of times I don't read questions carefully, misread words , misinterpretations and all, how you improved your accuracy, does revising theory helps, or more practicing questions, or may be give practice papers.

@Ronak Agarwal – Yes bro me too ! and actually this is often happen in mains , I did less mistakes while I gave Advance Test in my Tution tests , But Acurracy is largly decreased in mains , Due to careless study of questions ! I don't think that it is wise to try New Books or trying new questions for correcting accuruacy ! But I think It will be better if we do practising Papers in proper time , means which includes filling of OMR also ! We have 10 JEEmains paper 5 of 2013 and 5 of 2014 (including online and offline) , Also AIEEE 2012 and AIEEE 2011 Paper are also on same JEEMains Pattern . So I'am reguarly giving one Paper each day and then analylyse my mistakes and analyse what topics need's to be revise . Since It is impossible to revise notes, atleast maths and physics did not needs reading of theory notes ! But what you think ? Should still we should atleast take a qiuck look on notes ? and what else ?

@Deepanshu Gupta – can you tell me where you got online jee main papers? for practice @Deepanshu Gupta

@Mvs Saketh – Sorry for Late reply , actully I'am now avoiding using Brilliant , this is almost last day !

For JEEMains 2014 Question Papers click here JEEmains2014

For JEEmains 2013 question Papersclick here JEEmains2013

after cliking on second link(JEEMains 2013) , scroll down the page , and you will find a red Mark , click on that and you will find one another link after again scrolling down the page , which is written after 4 dates of JEEMAINS 2013 ! click on that and download all 4 papers ! Hopes This Helps ! @Mvs Saketh

Deepanshu Gupta - 6 years, 2 months ago

Indeed, they should have looked into it , unfortunately they did'nt

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$