A cubical block of wood, 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.50 cm below the interface (?Fig. E12.33?). The density of the oil is 790 kg/m3. (a) What is the gauge pressure at the upper face of the block? (b) What is the gauge pressure at the lower face of the block? (c) What are the mass and density of the block?

Solution 31E Step 1: Introduction : In this question, we have a wooden cube which is floating on the interface of oil and water In the first part we need to find the gauge pressure on the upper part of the cube In the second part we need to find the gauge pressure on the lower part of the cube In the third part we need to find the mass and density of wood Data given Length of the cube L = 10 cm Length immersed in oil L O 1.50 cm Density of the oil o = 790 kg/m 3 Let us consider the figure given Step 2 : We need to find the gauge pressure on the upper part of the wood It is given by PT P =o gh o o We have h = 0.015 m 0 Substituting values we get PT P =o790 kg/m × 9.8 m/s × 0.015 m P P = 116 Pa T o Hence we have gauge pressure on top of the wood as 166 Pa We need to find the gauge pressure on the lower part of the wood It is given by PB P =o gho+ oh w w hw= 10 cm = 0.1 m 3 3 w= 1 × 10 kg /m Substituting values we get 3 2 3 3 2 P B P = o90 kg/m × 9.8 m/s × 0.1 m + (1 × 10 kg /m × 9.8 m/s × 0.015 m) P P = 774.2 Pa + 147 Pa B o PB P =o921 Pa Hence we have gauge pressure on bottom of the wood as 921 Pa