You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 4.15 m/s2. If your apparatus floats in the oceans on earth with 25.0% of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi?

Solution 28E Step 1: Acceleration due to gravity on earth, g = 9.8 m/s 2 Density of ocean water, d ocean 1029 kg/m 3 Equation for density of a substance, d = M/V Where, M - Mass of the substance V - Volume of the substance Therefore, Mass of the apparatus, M = Volume × d oceann earth Provided, only 25% of its volume is submerged. Then volume = 0.25 V 3 Therefore, mass, M = 1029 kg/m × 0.25 V - ------------------- (1) Step 2: Density of glycerine, d glycerine260 kg/m 3 Acceleration due to gravity of Caasi, g = 4.15 m/s 2 Therefore, Mass of the apparatus, M = Volume × d in Caasi glycerine Suppose the volume submerged is = x V Therefore, mass, M = 1260 kg/m × x V -------------------- (2)