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A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density =0.9986 g/mL). The readings are 860.2 g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is 21.45 g/cm^3, what should her conclusion be? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)

Respuesta :

Explanation:

According to Archimede's principle, when an object is submerged in a liquid then the force of buoyancy experienced by it is equal to the weight of liquid that is displaced by the object.

Also, it is known that density is the presence of mass in per unit volume.

Hence, equation for density of the given crucible is as follows.

                   d = [tex]\frac{m_{air} - m_{water}}{V}[/tex]

                 [tex]0.9986 g/mL = \frac{860.2 - 820.2 g}{V}[/tex]

                        V = 40.06 mL

Hence, density of the crucible in air will be as follows.

                    D = [tex]\frac{\text{mass of crucible in air}}{Volume}[/tex]

                        = [tex]\frac{860.2 g}{40.06mL}[/tex]

                        = 21.47 g/mL

As the density of platinum is given as 21.45 [tex]g/cm^{3}[/tex] and the calculated value is 21.47 g/mL. Hence, these values are close enough.

Thus, we can conclude that her conclusion should be that the given masses should be measured with a sensitive scale.

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