Question

A U tube with both ends open to the atmosphere, is
partially filled with water. Oil, which is immiscible
with water, is poured into one side until it stands at a
distance of 10 mm above the water level on the other
side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is​

Answer 1

$\bf\huge\underline\red{Solution}$

Gauge pressure -

Pressure diffrence between hydrostatic and atmospheric pressure

- wherein

$\sf \implies P-P_{0}= ho gh$

$\sf \: P-P_{0}= gauge : pressure$

Pressure of two points lie in the same horizontal level should be same and P= pgh

Both ends of tube is open, so the pressure on both the free surface must be equal.

$\rightarrow \sf \: P_{1}=P_{2}$

$\sf\Rightarrow h_{oil}\:\: \rho_{oil}\:\:g=h_{water}.\rho_{water}g$

$\sf\Rightarrow\rho_[oil=\frac{h_{water}\:\rho_{water}}{h_{oil}}]$

$\sf\rho _{oil}=\frac{(65+65)\times 1000}{65+65+10}=928 kgm^{-3}$

Therefore, the Option 4) 928 kg m-3 This option is correct.

Answer 2

Concept :

Definition : Pressure is defined to be the amount of force exerted per area.

Solution :

Pressure difference between hydrostatic and atmospheric

$\underline{ \boxed{ \sf{ \purple{ P - P0 = hogh}}}}$

$\underline{ \boxed{ \sf{ \purple{P - P0 = gavge : pressure}}}}$

• P = Pgh

$\underline{ \boxed{ \sf{ \red{So \: Let's \: start \: solving}}}}$

$\sf \implies \: p1 = p2$

$\sf \: hᴏɪʟ \: Pᴏɪʟ g = hᴡᴀᴛᴇʀ.Pᴡᴀᴛᴇʀ$

$\underline{ \boxed{ \sf{ \purple{P= [oil = \frac{hᴡᴀᴛᴇʀ \: Pᴡᴀᴛᴇʀ}{hᴏɪʟ} ]}}}}$

$\underline{ \boxed{ \sf{ \pink{Pᴏɪʟ = \frac{(65 + 65) \times 1000}{65 + 65 + 65} = 928 \: kg {m}^{ - 3} }}}}$

So, The option 4) 928 kgm^-3 This option is correct dear ❤