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) A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m3) is raised up so the rock is totally submerged in the water. The scale now reads . What is the density of the rock? A) 2.50 × 103 kg/m3 B) 1.60 × 103 kg/m3 C) 2.33 × 103 kg/m3 D) 2.67 × 103 kg/m3 E) 3.00 × 103 kg/m3

Respuesta :

Answer:

The density of the rock is [tex]2.67\times10^{3}\ kg/m^3[/tex]

(D) is correct option.

Explanation:

Given that,

Force = 20.0 N

Density = 1000 kg/m³

Suppose the scale new reads 12.5 N

We need to calculate the mass of rock

Using formula of force

[tex]F= mg[/tex]

[tex]m=\dfrac{F}{g}[/tex]

Put the value into the formula

[tex]m=\dfrac{20.0}{10}[/tex]

[tex]m=2\ kg[/tex]

Scale reads 12.5 N after rock is totally submerged so mass of rock after submerged

We need to calculate the mass of rock

Using formula of force

[tex]F= mg[/tex]

[tex]m=\dfrac{F}{g}[/tex]

Put the value into the formula

[tex]m=\dfrac{12.5}{10}[/tex]

[tex]m=1.25\ kg[/tex]

The scale reads 12.5 N = 1.25 kg so it is displacing 0.75 kg of water

We need to calculate the volume of rock using volume of water it displaces:

Using formula of volume

[tex]Volume\ of \ rock=\dfrac{0.75}{1000}[/tex]

[tex]V=7.5\times10^{-4}[/tex]

We need to calculate the density of the rock

Using formula of density

[tex]\rho=\dfrac{m}{V}[/tex]

Put the value into the formula

[tex]\rho= \dfrac{2}{7.5\times10^{-4}}[/tex]

[tex]\rho=2666.66\ kg/m^3[/tex]

[tex]\rho=2.67\times10^{3}\ kg/m^3[/tex]

Hence, The density of the rock is [tex]2.67\times10^{3}\ kg/m^3[/tex]

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