Question

A meter stick A hurtles through space at a speed v = 0.25c relative to you, with its length aligned with the direction of motion. You stand on Earth and have another meter stick B with its length aligned with the direction of motion of meter stick A. You measure the length of meter stick A to be 1 m. What is the length of meter stick B, L_B, as seen in the rest frame of meter stick A?

Answer 1

Answer:

$L_0\approx1.0328\ m$

Explanation:

Given:

• relativistic length of stick A, $L=1\ m$

• relativistic velocity of stick A with respect to observer, $v=0.25c=7.5\times 10^{7}\ m.s^{-1}$

Since the object is moving with a velocity comparable to the velocity of light  with respect to the observer therefore the length will appear shorter according to the theory of relativity.

Mathematical expression of the theory of relativity for length contraction:

$L=\frac{L_0}{\gamma}$

where:

L = relativistic length

$L_0=$ original length at rest

$\gamma =$ Lorentz factor $=\frac{1}{\sqrt{1-\frac{v^2}{c^2} } }$

$\Rightarrow 1=\frac{L_0}{\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }}$

$L_0=\frac{1}{\sqrt{1-\frac{(0.25c)^2}{c^2} } }$

$L_0\approx1.0328\ m$