A uniform cylindrical hydrometer of mass 20g and cross sectional area 0.54cm2 floats upright in a liquid. If 25cm of its length is submerged, calculate the ...

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When a hydrometer floats in a liquid, it displaces an amount of liquid equal to its own volume, and the weight of the liquid displaced acts as an upthrust to balance the weight of the hydrometer. If the hydrometer floats with 25 cm of its length submerged, then the volume of liquid displaced by the hydrometer is equal to the volume of the submerged part of the hydrometer, which is given by the formula V = Al, where A is the cross-sectional area of the hydrometer and l is the length submerged. So, the volume of liquid displaced is V = 0.54 cm² x 25 cm = 13.5 cm³. The weight of the liquid displaced is equal to the weight of the hydrometer, which is given by the formula W = mg, where m is the mass of the hydrometer and g is the acceleration due to gravity. So, W = 0.02 kg x 9.81 m/s² = 0.1962 N. The relative density of the liquid is given by the formula ρ_liquid/ρ_water = F_upthrust/W, where F_upthrust is the upthrust on the hydrometer due to the liquid. The upthrust is equal to the weight of the liquid displaced, which we have already calculated to be 0.1962 N. So, ρ_liquid/ρ_water = 0.1962 N / (0.54 cm² x 25 cm x 9.81 m/s² x 1 g/cm³) = 1.48 Therefore, the relative density of the liquid is 1.48. Answer (b) 1.48.