Physics

Problem

A uniform wooden prism has a rectangular cross-section of area

25\,\text{cm}^{2}

and a length of

20\,\text{cm}

. It is gently lowered, with its length vertical, into a deep tank containing two immiscible liquids. The lower liquid is glycerine of density

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

and the upper liquid is paraffin oil of density

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

. At equilibrium the prism is found to be submerged to a depth of

6\,\text{cm}

in glycerine and

7\,\text{cm}

in paraffin oil. (i) Calculate the density of the wood. (ii) Find the length of the prism that remains above the surface of the paraffin oil.