Question

If a rod is moving at a velocity equal to 1/2 the speed of light parallel to its length, what will a stationary observer observe about its length?

Answer 1

The length of the is 0.866 L₀.

Step-by-step explanation:

Given that,

Velocity of rod = half the speed of light

We need to calculate the length

Using formula of length

`L=L_(0)\sqrt{1-((v)/(c))^2}`

Where, L= length

v = velocity of rod

c = speed of light

L₀ = observer length

Put the value into the formula

`L=L_(0)\sqrt{1-(((0.5c)^2)/(c^2))}`

`L=L_(0)√(1-(0.5)^2)`

`L=0.866L_(0)`

The length of the rod will decreases

Hence, The length of the rod is 0.866 L₀.

Answer 2

The length of the rod will decrease.

Step-by-step explanation:

According to Einstein's relativity theory we know that

`L=L_0*√(1-(v/c)^2)`

where Lo= initial length of the rod

v= velocity of moving rod= c/2

c= velocity of light

put v= c/2 we get

L= 0.866 L₀

Therefore, The length of the rod will decrease.