Question

A rod 1 metre long is moving along its lenght with a velocity of 0.6c .Calculate its lenght as it appear to an observer.
1) On the earth.
2) Moving with rod itself.

Answer 1

length= .8m and 1m resp

Answer 2

Answer:

(1) The length of the rod observed is 0.8 m

(2) The length of the rod observed is 1 m

Explanation:

The length of the rod $L_{o}=1 m$

The velocity of the rod is v=0.6 c

The speed of light is c

PART(A)

As the velocity of the rod is very high

So if we observe the rod from the other reference of frame then the length of the rod will be shorter than its original length due to theory of relativity.

The relative formula for the length is,

$L=L_{o}\sqrt{1-\dfrac{v^2}{c^2}}\\L=1\sqrt{1-\dfrac{(0.6c)^2}{c^2}}\\L=\sqrt{1-0.6^2}\\L=\sqrt{1-0.36}\\L=\sqrt{0.64}\\L=0.8\ m$

PART(B)

If the observer is moving with the rod itself means that the rod is at same reference of frame then the length of the rod observed by the observer is same as $L_{o}=1\ m$