Question

An experimenter places a piece of solid metal weighing 255g into a graduated cylinder which she then fills with mercury. After weighing the cylinder and its contents, she removes the solid and tops of the cylinder with mercury. The cylinder and its contents weigh 101g less than before. The density of Hg is 13.6g/cm^3 . What is the density of the solid metal

Answer 1

Answer: the density of the solid metal is 22.5176 g/cm

Explanation:

Given that;

mass of solid metal = 255 g

the cylinder and its contents weigh 101g less than before

also given that density of mercury = 13.6 g/cm³    

Volume of the solid metal = volume of mercury which was absent in the first weighing

so let volume = Vcm³

Mass of mercury which was absent in the first weighing = density × volume

= 13.6 g/cm³  × Vcm³ = 13.6V g

now since the cylinder and its contents weigh 101g less than before,

it means the difference in mass between the solid and metal and the mass of mercury is equal to 101 g

so

255 - 13.6V g = 101g

13.6V g = 255 g - 101 g

13.6V  = 154

V = 154 /  13.6

V = 11.3245 cm³

Now Density of solid metal will be;

⇒ mass / volume

= 255 / 11.3245

= 22.5176 g/cm

Therefore, the density of the solid metal is 22.5176 g/cm

Answer 2

This question involves the concepts of volume, mass, and density.

The density of the solid metal is "22.5 g/cm³".

First, we need to find the volume of the solid metal. The volume of solid metal must be equal to the volume of mercury absent when solid metal was present in the cylinder. The difference between masses can be given as follows:

$255\ g + Mass\ of\ Mercury\ in\ remaining\ volume=\\Mass\ of\ mercury\ occupying\ volume\ of\ solid\ +Mass\ of\ Mercury\ in\ remaining\ volume+101\ g\\\\255\ g =(13.6\ g/cm^3)(V)+101\ g\\\\V=\frac{255\ g-101\ g}{13.6\ g/cm^3}\\\\V=11.323\ cm^3V =$where,

V = volume of solid

Therefore, the density of solid will be:

$Density = \frac{mass}{volume}=\frac{255\ g}{11.323\ cm^3}$

Density = 22.5 g/cm³

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