Question

If the volume of a cube of side \( L_0 \) is \( L_0^3 \) as observed by an observer at rest relative to it, the volume as observed from a reference frame moving with uniform velocity \( 0.8c \) in a direction parallel to an edge of the cube will be:

• A. \(L_0^3 \)
• B. \( 0.6 L_0^3 \)
• C. \( 0.216 L_0^3 \)
• D. \( 0.512 L_0^3 \)

Hint:

Length contraction only affects the dimension **parallel to motion**, while perpendicular dimensions remain unchanged.

Answer 1

The Correct Option is B

Due to Lorentz contraction, only the length along the direction of motion contracts. The length contraction formula is:
\[ L = L_0 \sqrt{1 - \frac{v^2}{c^2}} \] For \( v = 0.8c \):
\[ L = L_0 \sqrt{1 - 0.64} = L_0 \times 0.6 \] The volume contracts as:
\[ V = L_0^2 \times L = L_0^3 \times 0.6 \] \[ V = 0.64 L_0^3 \]