In a laboratory

PHYSICS · Subjective · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

In a laboratory, a cylindrical tank is open to the atmosphere and contains two immiscible liquids. A layer of unknown oil of thickness

0.45\,\text{m}

floats above glycerine of thickness

0.60\,\text{m}

and density

1260\,\text{kg}\,\text{m}^{-3}

. The bottom of the tank is connected to one limb of a U-tube manometer containing mercury of density

13\,600\,\text{kg}\,\text{m}^{-3}

. The other limb of the manometer is open to the atmosphere. The mercury levels in the two limbs differ by

0.070\,\text{m}

, the limb connected to the tank being lower. (a) Establish an equation that relates the density

\rho

of the unknown oil to the observed difference in mercury levels. (b) Hence calculate the density of the unknown oil.