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A U – tube is partially filled with water . Oil which does not mix with water is next poured into one side until water rises by 2.5 cm on the other side . if the density of oil be 1.8 the oil level will stand higher the water level by 6.25 cm 12.5 cm 31.35 cm 20 cm

A U – tube is partially filled with water . Oil which does not mix with water is next poured into one side until water rises by 2.5 cm on the other side . if the density of oil be 1.8 the oil level will stand higher the water level by 
  1. 6.25 cm
  2. 12.5 cm
  3. 31.35 cm
  4. 20 cm

Grade:12

3 Answers

Vineeth Kumar
34 Points
8 years ago
6.25cm
Mitul Asher
28 Points
7 years ago
Dear Student, 
 

It is important to recall that as the water and oil levels are stationary the pressure exerted by both columns in the tube would be equal.

So,

P(water) = P(oil)

or

ρwghw = ρoilghoil

or
ρwg×25= ρmghoil

⇒hoil=1×250.8=31.25 cm

​Difference in the height will be 31.25 - 25  = 6.25 cm
Regards 

Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem below.
 
I think you got the question wrong as the density of the oil can never be higher than water for it to be at higher level than water, so for that very reason I am taking it to be 0.8. Also on taking the water depth variation as 2.5 cm, none of the option matches( In that case answer comes out to be 1.25 cm). Hence I will be taking it as 25 cm instead.
 
If the water level rises by 25 cm on the other tube then it also falls the same level in the same tube. Therefore the water level will differ by 50 cm.
Taking the water level in this tube as Datum.
Now Poil = Pwater
or, ρogho = ρwghw
or, 0.8 x ho = 1 x 50
Hence, ho = 62.5 cm
Hence, the oil level will stand higher than water level by an amount = 62.5 – 50 = 12.5 cm
 
Hope it helps.
Thanks and regards,
Kushagra

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