Question

En un recipiente con mercurio (13.6 gr/cm3) se sumerge completamente un cuerpo de 900 gramos de masa. AL medir su peso aparente este marca 2.94 newton en el dinamómetro. Cual es la densidad del cuerpo (kg/m3)

Answer 1

ρ = 20.4 kg / m³

Step-by-step explanation:

For this exercise we use Archimedes' principle, the thrust on a submerged body is equal to the weight of the released liquid

B = ρ g V_liquid (1)

let's write the equilibrium equation

F -W + B = 0

B = W -F

let's calculate

B = 0.900 9.8 - 2.94

B = 5.88 N

From equation 1

V_{liquid} =
`(B)/(\rho_(Hg) g)`

V_{liquid} =
`(5.88)/(13.6 \ 10^3 \ 9.8)`

V_{liquid} = 4.41176 10⁻⁵ m³

in this case it is indicated that the body is completely submerged

V_body = V_liquid = V

the definition of density is

ρ = m / V

ρ =
`(0.900 \ 10^(-3))/( 4.41176 \ 10^(-5) )`

ρ = 2.04 10¹ kg / m³

ρ = 20.4 kg / m³