If \(L^{3}_{0}\) is the rest volume of a cube, then volume viewed from a reference frame moving with uniform velocity v in a direction parallel to an edge of the cube is

Calculation:

Given that the reference frame is moving parallel to one edge of the cube:

The length along the direction of motion will contract according to the formula. L = L0 × (1 - v2 / c2)1/2 

 Here, L0 is the rest length and L is the contracted length.

However, the lengths perpendicular to the direction of motion remain unchanged.

Volume of the cube is:

V = Length × Width × Height

In this case:

Length along the direction of motion = L₀ × (1 - v² / c²)^1/2

Width and Height remain = L₀

⇒ V = L₀ × (1 - v² / c²)^1/2 × L₀ × L₀

⇒ V = L₀³ × (1 - v² / c²)^1/2