Question

obtain the volume of a cube, the proper length of each edges of which L when it is moving with the velocity v along of its edges

Answer 1

Answer:

According to question,

Edge length of a cube =l

Hence, cube has 12 edges.

So,sum of length of edges =12l

Hence formula for the sum of edge length =(12× one edge length)

Answer 2

Answer:

V = $\L^3[1-(\frac{V^{2} }{C^{2} })]^{1/2}$

Explanation:

Given:

The proper length of each edges is L of a cube

The velocity while moving is V along its edges.

To find:

The volume of cube

Solution:

According to classical physics, a body's inertial mass is independent of its velocity of light. It is considered a constant.

However, the special theory of relativity introduces the concept of mass variation with velocity.

According to special theory of relativity, the mass m of a body moving with relativistic velocity v relative to an observer is greater than its mass m when at rest.

Without going into their mathematical derivations, some interesting results of the special theory of relativity can be summarized as follows.

Given, length of the cube = L

⇒ Volume of cube is $V = L^{3}$

If the cubes moves with V velocity along its edges then,

⇒ V = $L^{3} \sqrt{1 - (\frac{V^{2} }{C^{2} }) }$

⇒ V  = $\L^3[1-(\frac{V^{2} }{C^{2} })]^{1/2}$

Hence, the volume of cube  V  = $\L^3[1-(\frac{V^{2} }{C^{2} })]^{1/2}$ .

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