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 `65mm` from its original level (see diagram). The density of the oil is:

A. `650 kg m^(-3)`
B. `425 kg m^(-3)`
C. `800 kg m^(-3)`
D. `928 kg m^(-3)`

Answer 1

Correct Answer - d
Thinking Process 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 surface must be equal.
i.e, `p_(1) = p_(2)`
`h_("oil").S_("oil") = h_("water").S_("water").g`
`S_("oil") = "specific density of oil"`
`S_("oil") = (h_("water").S_("water").g)/(h_("oil).g)`
From figure `S_(oil) = ((65 + 65) xx 1000)/((65 + 65+10))`
`= 928 kgm^(-3)`