Question

You measure the volume of a cube at rest to be V0. You then measure the volume of the same cube as it passes you in a direction parallel to one side of the cube. The speed of the cube is 0.980c, so γ ≈ 5. The volume you measured is close to which of the following choices?V0/125 or V0/5 or V0 or 5V0 or 125V0

Answer 1

Answer:

V  =  V₀ / 5

Step-by-step explanation:

At rest V₀ is volume measured of a cube

When an observer measures it at high speed  ( 0.98*c ) the length he measures from outside, if he can looks and measures the two points start and ending points of the parallel edge simultaneously,  is shorther ( such effect is known as Lorentz contraction. In this particular case problem statement  give  γ ≈ 5

γ  =  1  / √( 1 - v²/c²)       γ  =  1  / √1  -( 0.98)c²/c²     γ  =  1  /√1-0,9604

γ  =  1 /√ 1 - 0.9604     γ  =  1 /√0.0396    γ  ≈ 5

As the contraction only occur in the sense of the movement then the volume of the cube would be

V = (edge)²* (edge/5)      or   V  =  V₀ / 5