# The dynamometer to which the body is suspended with a density p = 2.5 g / cm3 in a cube shows 5H

The dynamometer to which the body is suspended with a density p = 2.5 g / cm3 in a cube shows 5H, When the body is immersed in water, the dynamometer readings are 3 N and in an unknown liquid -3.4 N. Determine a) body mass b) body volume) c) the density of the unknown liquid is rwice = 1000 kg / m3.

ρ = 2.5 g / cm ^ 3 = 2500 kg / m ^ 3.
F1 = 5 N.
F2 = 3 N.
ρw = 1000 kg / m ^ 3.
F3 = 3.4 N.
g = 9.8 m / s ^ 2.
m -?
V -?
ρн -?
F1 = m * g.
m = F1 / g.
m = 5 N / 9.8 m / s ^ 2 = 0.51 kg.
F2 = F1 – Farch.
Farch (in) = ρw * g * V.
F2 = F1 – ρw * g * V.
V = (F1 – F2) / ρw * g.
V = (5 N – 3 N) / 1000 kg / m ^ 3 * 9.8 m / s ^ 2 = 0.0002 m ^ 3.
F3 = F1 – Farch (n).
Farch (n) = ρн * g * V.
F3 = F1 – ρн * g * V.
ρн = (F1 – F3) / V * g.
ρн = (5 N – 3.4 N) / 0.0002 m ^ 3 * 9.8 m / s ^ 2 = 816 kg / m ^ 3.
Answer: m = 0.51 kg, V = 0.0002 m ^ 3, ρn = 816 kg / m ^ 3.

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