## yrelhan4 2 years ago A simple U-tube that is open at both ends is partially filled with water (d=1000kg/m^3). now a liquid of density d is poured into left arm. it d of liquid surface in the left does not mix with water. it is observed that height of liquid surface in the left arm is 2cm more than height of water surface in left arm. what is density d of the liquid?

1. yrelhan4

ok so whenever i have done these kind of problems i have always known length of liquid column in the left arm. but not in this question. so how should i start?

2. yrelhan4

@Mashy

3. Mashy

wait.. lemme read the question properly!! :P

4. Mashy

draw.. first draw.. !!

5. yrelhan4

correction: water surface in the right arm.

6. Mashy

and are you sure its the 2cm more than LEFT arm itself?? so basically its saying the length fo the column of the liquid itself is 2cm :O :O :O!!!!

7. yrelhan4

|dw:1361214865922:dw|

8. yrelhan4

length of column isnt 2cm. in the second question they have asked length of the column.

9. Mashy

|dw:1361214958351:dw|

10. Mashy

does that make sense?

11. yrelhan4

it does. but there is still a constant 'a'. how do i eliminate that? where do i apply the pressure equation?

12. Mashy

wait lemme think :P hey what happens if you apply pressure equation for the UPPER LINE level?? left side is pressure due to atm and 2 cm of liquid right side is pressure due to atm only

13. yrelhan4

:O idk what happens. nice man. you are intelligent. :P

14. Mashy

no.. ther is something wrong.. there is something m missing.. you can't do that.. !! :O

15. yrelhan4

why not?

16. Mashy

what why not?? if you equate them.. you ll get the pressure due to 2cm liquid to be zero!!.. cause patm cancel out on both sides!

17. yrelhan4

hmm. sure. :P

18. Mashy

am i too sleepy!??? i just went to my textbooks.. and you can do that for all problems!! consider at the surface of the liquid in the column which is lower.... !?? tell me ?? whats wrong if we do that ?

19. yrelhan4

|dw:1361216017495:dw|

20. Mashy

not that.. !! |dw:1361216075828:dw|

21. Mashy

you could do that for all problems.. and the density of all liquids would come zero! :-/

22. yrelhan4

i'm sorry. no ideas whats wrong. i have done 5-6 problems like this and i have never seen a the level at the surface of a liquid. why not? i dont know.

23. Mashy

even i dunno!!.. this is insane.. anwyays.. i think you can tke for the lower line ... in that case, the height of the liquid would be a +2... and the height of the water would be just a.. lol.. i dunno if that works :D

24. Mashy

maybe you shouldnt consider at the surface... cause on one side its liquid and the other side its air.. so the pressures really need not be the same!!

25. Mashy

yea that must be it :P

26. yrelhan4

haha. alright. :P

27. Mashy

but still thats not convincing me.. DAMN YOU.. its already 1.15 am here and now i can't sleep!! argggg

28. rajathsbhat

it's simple guys

29. yrelhan4

haha. spend sometime on this question. maybe it'll help you to sleep. :P

30. Mashy

plz rajath.. tel why !!

31. rajathsbhat

dg(a+2)=1000ga. makes sense? refer to mashy's diagram.

32. Mashy

yea but how will you solve that??????? but my question is.. why can't we ever consider at the surface???

33. yrelhan4

lol. how would you eliminate a? another equation? what would it be?

34. Mashy

something is missing in your question.. too ambiguous !! ll post a new question.. wait!!

35. rajathsbhat

^ikr

36. yrelhan4

well its what the book says. idk,

37. rajathsbhat

ooh i got it. just a sec

38. Mashy

quick.. i need to sleep!! :P

39. rajathsbhat

use the buoyant force equation for the new liquid. you get dgA(a+2)=1000gAa get an equation for d in terms of a and substitute it into the first equation.

40. rajathsbhat

A is the area of cross section of the tube

41. Mashy

doesn't that give you back the same equation!?!? :P

42. rajathsbhat

lolol i just realized that xD

43. yrelhan4

lol. it does. :P

44. Mashy

you are just running in circles.. omg.. our smartscores are at the stake here rajath's being the most LOLZZ :D

45. rajathsbhat

hey but there is this one thing. why does it look like the pressure exerted by the 2cm column is 0?

46. Mashy

thats the problem m trying to tackle from that time.. if you consider pressure equation at the surface.. every problem gives you answer as zero.. something is horribly wrong with logic.. check my question.. its at the top!!

47. yrelhan4

48. rajathsbhat

lol mashy i know i have to brush up on my skillzzzz :P but i'm not letting this one go

49. yrelhan4

thats the spirit :P

50. yrelhan4

@Vincent-Lyon.Fr

51. Mashy

You calling in heavy reinforcements i see :D

52. Mashy

dude.. i seriously believe the question does not give enough data!!.. try thinking practically!!!.

53. yrelhan4

hmm maybe. i think i'll let this one go. :P

54. rajathsbhat

yeah something tells me that 'a' should've been given. But the way this problem is sentenced makes me think otherwise.

55. Mashy

i am more worried about what i was addressing lolzzz..!!! but i think the solution to my problem is.. that you cannot use pressure equation at that level, the surface or any level above that.. cause unlike liquids.. we don't have an equation for the pressure due to atmosphere for a depth !!.. so maybe its forbidden..!! but i really need a better answer !!

56. yrelhan4

anyway, i'm gonna go now. you guys scratch your brains. :P

57. Mashy

no m leaving as well.. thanks for dragging me into this.. really.. now i have something to think about.. so ll give you a medal :D and i ll fan yu :D

58. rajathsbhat

i got it! i know why we can't say that the pressure due to the 2cm is not 0.

59. Mashy

you mean what we can't say that the pressure due to 2cm IS zero?

60. rajathsbhat

yes

61. Mashy

dazzle me .. quick quick!!!

62. Mashy

did you fall asleep or something?!?!?

63. rajathsbhat

lmao ok think of the whole liquid column as a solid. the 2cm column is like the part of an iceberg that sticks out of the water surface. it's being held up and not allowed to sink beyond that level because the part of the same liquid below it is applying a force equal to it's weight.

64. rajathsbhat

and how does this solve the problem of pressure you ask. I'll tell you how.

65. rajathsbhat

didn't we learn that the molecules inside a liquid are pulled equally by the other molecules? (i remember learning this while learning about surface tension) so, AT THAT LEVEL and AT EVERY LEVEL IN THAT MYSTERY LIQUID, the pressure is the same and it's equal to the atmospheric pressure.

66. Mashy

wait wait wait.. !!

67. rajathsbhat

I could be COMPLETELY WRONG but lemme think about it a little bit more.

68. yrelhan4

*yawn* goodnight both of you! :P

69. Mashy

first of all you can't treat it like a solid.. cause fluid mechanics doesn't hold good for solid!! :P.. but wait.. m thinking!!

70. Mashy

yrelhan4.. if i ever meet you .. remind me to first kill you :D

71. Mashy

|dw:1361219680403:dw| if what you are saying is true.. (whatever that is :D) if it applies at level 1, why doesn't it apply at level 2?? why isn't level 2 at atm pressure??

72. Mashy

|dw:1361219869615:dw| a better picture :P

73. rajathsbhat

you're right....obviously there is a gap in my understanding of this part of the universe.

74. Mashy

or maybe we found a flaw in mechanics.. quickly lemme patent this.. before you steal away my query :D

75. rajathsbhat

Mark my words - I will get to the bottom of this (if vincent doesn't answer first :P) in less than 24 hours from now. (and lol ^)

76. Mashy

K i really need to sleep now.. so ll go now .. .bye bye.. lets discuss tihs with someone who actually knows physics lol :D !! m ashamed to call myself physics teacher now!

77. rajathsbhat

see ya tomorrow. this is a wake up call for me. Time to whip out those dusty old physics books :P

78. yrelhan4

ok so got it guys. the options are 1000,1200,1400,800 kg/m^3 according to equation dg(a+2)=1000ga, obviously d<1000, so that would mean d=800. so that is that. thank you for wasting your time on this question. :P cheers!