Answer:
4341.44763 kg/m³
Explanation:
[tex]\rho'[/tex] = Actual density of cube = 1800 kg/m³
[tex]\rho[/tex] = Density change due to motion
v = Velocity of cube = 0.91c
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
Relativistic density is given by
[tex]\rho=\frac{\rho'}{\sqrt{1-\frac{v^2}{c^2}}}\\\Rightarrow \rho=\frac{1800}{\sqrt{1-\frac{0.91^2c^2}{c^2}}}\\\Rightarrow \rho=\frac{1800}{\sqrt{1-0.91^2}}\\\Rightarrow \rho=4341.44763\ kg/m^3[/tex]
The cube's density as measured by an experimenter in the laboratory is 4341.44763 kg/m³
