Question

A cube has a density of 1800 kg/m3 while at rest in the laboratory. What is the cube's density as measured by an experimenter in the laboratory as the cube moves through the laboratory at 89.0 % of the speed of light in a direction perpendicular to one of its faces?

Answer 1

3947.7 kg/m³

Step-by-step explanation:

The relativistic density can be calculated using below expression;

ρ = ρ' /[√( 1 - v²/c²)]

where,

ρ = Change in Density as a result of motion

ρ'= Actual density of cube

ρ' is given as = 1800 kg/m³

v = Velocity that the cube moves = 0.89c

c = Speed of light

c= 3×10^8 m/s

ρ = ρ' /[√( 1 - v²/c²)]

if we substitute the given values we have

ρ= 1800/ √ 〈1- 0.89c²/ c²〉

ρ=3947.7 kg/m³

Hence, the cube's density is 3947.7 kg/m³