Question

Special Relativity, A rod

Answer 1

A rod of proper length \(l_0\) is at rest in a frame S'. It lies in the (x',y') plane and makes an angle \(\sin^{-1}\left( \frac{ 3 }{ 5 } \right)\) with x' axis. If S' moves with constant velocity v parallel to the x - axis of another frame S:

a) What must be the value of v if as measured in S the rod is at 45 degrees to the x - axis?

b) What is the length of the rod as measured in S under these conditions?

Answer 2

a)

\[\gamma = \dfrac{1}{\sqrt{1-\beta^2}}=\dfrac{5}{3}\implies \beta = 0.8 \]

so \(v = 0.8c\)

Answer 3

b)
\(3\sqrt{2}\)

Answer 4

@ganeshie8

So if we want 45 degrees to x-axis, then we wish that the length four to be length 3. Therefore we want \(\gamma = \frac 4 3\) rather than \(\gamma = \frac 5 3\) ?

Answer 5

Ahh right! thanks for the catch :)