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 relative density of the oil with respect to water is______

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Detailed Solution

Pressure of two points lie in the same horizontal level should be same and p=hdg.
Both ends of the U-tube are open, so the pressure on both the free surfaces must be equal,
i.e $p_{1} = p_{2}$
$h_{o i l} . S_{o i l} g = h_{w a t e r} . S_{w a t e r} . g$
Where, $S_{o i l}$ = specific density of oil.
$\Rightarrow S_{o i l} = \frac{h_{w a t e r} . S_{w a t e r} . g}{h_{o i l} . g}$
From figure $S_{o i l} = \frac{(65 + 65) \times 1000}{(65 + 65 + 10)}$
$= 928 k g m^{- 3}$