A rod of length L₀ makes an angle θ₀ with the Y-axis in its rest frame while the rest frame moves to the right along the X-axis with relativistic speed v with respect to lab frame. If $$\gamma = {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)^{ - \frac{1}{2}}},$$ the angle in the lab frame is

A) $$\theta = {\tan ^{ - 1}}\left( {\gamma \tan {\theta _0}} \right)$$ B) $$\theta = {\tan ^{ - 1}}\left( {\gamma \cot {\theta _0}} \right)$$ C) $$\theta = {\tan ^{ - 1}}\left( {\frac{{\tan {\theta _0}}}{\gamma }} \right)$$ D) $$\theta = {\tan ^{ - 1}}\left( {\frac{{\cot {\theta _0}}}{\gamma }} \right)$$

Answer & Solution

Correct Answer: Option B

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A rod of length L0 makes an angle 0 with the...

A rod of length L0 makes an angle θ0 with the Y-axis in its rest frame while the rest frame moves to the right along the X-axis with relativistic speed v with respect to lab frame. If $$\gamma = {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)^{ - \frac{1}{2}}},$$ the angle in the lab frame is

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A rod of length L₀ makes an angle θ₀ with the Y-axis in its rest frame while the rest frame moves to the right along the X-axis with relativistic speed v with respect to lab frame. If $$\gamma = {\left( {1 - \frac{{{v^2}}}{{{c^2}}}} \right)^{ - \frac{1}{2}}},$$ the angle in the lab frame is