A uniform U tube is partially filled with water Oil of dens

A uniform U - tube is partially filled with water. Oil, of density 0.67 g/cm^3, is poured into the right arm until the water level in the left arm rises 2 cm. What is the length of the oil column Answer in cm

Solution

1) At the beginning, there was just water, and both ends of the tube had the same level.
2) Then oil was poured on the right-hand side (RHS). Let us call the column-length of oil poured in, P.
3) As a result, the water level on the RHS sinks by column-length X.
4) Because the total amount of water in the tube is unchanged, the water level on the left-hand side (LHS) must rise by the same column-length, X. (So we see that X = 2 cm.)
5) On the RHS, the new water level is X below what it was before; and on the LHS, the new water level is X above what it was before. Therefore, the new water level on the LHS is 2X above the new water level on the RHS. This means that the 2X of water on the LHS side must balance, in weight, the P of oil on the RHS:
2X * 1 = P * (0.67) =
=> P = 5.97 cm ~ 6 cm

So the length of the oil column is ~ 6cm