# 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 Option 1) 650 kg m-3 Option 2) 425 kg m-3 Option 3) 800 kg m-3 Option 4) 928 kg m-3

@7561r

Gauge pressure -

Pressure diffrence  between hydrostatic and atmospheric pressure

- wherein

$P-P_{0}= \rho gh$

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

Pressure of two points lie in the same horizontal level should be same and $P=\rho gh$

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

$P_{1}=P_{2}$

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

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

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

Option 1)

650 kg m-3

This option is incorrect.

Option 2)

425 kg m-3

This option is incorrect.

Option 3)

800 kg m-3

This option is incorrect.

Option 4)

928 kg m-3

This option is correct.

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