Question

A cube with sides of proper length lo is viewed from a reference frame moving with velocity v, parallel to an edge of the cube. The expression for the volume of the cube for the observer is __________

(a) Lo^3

(b) Lo^3\(\sqrt{1-\frac{v^2}{c^2}}\)

(c) Lo^3\((1-\frac{v^2}{c^2})^{3/2}\)

(d) Lo^3\((1-\frac{v^2}{c^2})\)

I have been asked this question during an interview.

My doubt is from Lorentz Transformation Equations in section Ultrasonics & Relativity of Engineering Physics I

Answer 1

Correct choice is (a) Lo^3

Easy explanation: The rest volume of the cube is Lo^3. However, as the observer is moving at a high speed, one of the edges of the cube contracts. The rest of the edges, however, retain their proper length.

Thus, the edge of the cube reduces to l0\(\sqrt{1-\frac{v^2}{c^2}}\)

Volume = Lo^3\(\sqrt{1-\frac{v^2}{c^2}}\).