Question

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 16.0 N. When completely submerged in water, its apparent weight is 13.4 N. What is the volume of the object? m3 The density of ethyl alcohol at zero degrees Celsius is 806 kg/m3.

Answer 1

Density of water (ρ_water) =1000kg/m^3

Density of alchol (ρalcohol) =806kg/m^3

Acceleration due to gravity is (g) = 9.80m/s^2

An object is completely submerged within a fluid, itsapparent weight in the fluid is equal to its true weightmg minus the upward-acting buoyant force. According to Archimedes’ principle, the magnitude of thebuoyant force is equal to the weight of the fluid displaced by the object.

The weight of the displaced fluid depends on the volume of theobject. We will apply this principle twice, once for the objectsubmerged in each fluid, to find the volume of the object.

Apparent weights is given by

                                    16.0 N= mg

-p_alcholgV   ...................(1)

And inwater                13.4 N = mg

_-PwatergV.......................(2)

From the equations (1) and (2) we get the volumw of theobject is

         V = (16.0N -13.4N)/g(p_water-p_alchol)    then put values and calculate..

V= (2.6)/9.81(1000-806)

V= 2.6/1903.14

V= 1.367*10^-3 m^3 (Answer)

I hope help you !!