Question

A U tube in which both ends are open to the atmosphere is partly filled with water. Oil, which does not mix with water, is poured into one side until it stands a distance d = 15.0mm above the water level on the other side which has meanwhile risen a distance 67.5 from its original level. The density of the oil is:

• A. 600 kg/m³
• B. 750 kg/m³
• C. 840 kg/m³
• D. 900 kg/m

Answer 1

Answer: (D)

900 kg/m

Answer 2

In equilibrium pressure at A & A' are equal as both are at same horizontal level in the same liquid. As water has risen

by 'a' in right column, it has descended by a in left column.

Thus water level is 2a from A' and length of oil column is

2a + d. Equating pressures at A & A'.

P₀ + ρ_wg2a = P₀ + ρ₀g(2a + d)

ρ_oil = ρ_w $\frac{2a}{2a + d}$

= 1000. $\frac{2 \times 67.5}{2 \times 67.5 + 15}$=1000. $\frac{135}{150}$

= 900 kg/m