Question

The length of a measuring rod is 1m when it is at rest What will be its length if it is moving
with a velocity one third of the speed of light?
​

Answer 1

Given that,

Rest length = 1 m

Speed of rod $v_{r}=\dfrac{1}{3}\times v_{c}$

We need to calculate the length

Using formula of length

$l=l_{0}\sqrt{1-(\dfrac{v}{c})^2}$

Put the value into the formula

$l=1\times\sqrt{1-(\dfrac{\dfrac{1}{9}c^2}{c^2})}$

$l=1\times\sqrt{1-(\dfrac{1}{9})}$

$l=0.94\ m$

Hence, The length is 0.94 m

Answer 2

Given that,

Rest length = 1 m

Speed of rod $v_{r}=\dfrac{1}{3}\times v_{c}$

We need to calculate the length

Using formula of length

$l=l_{0}\sqrt{1-(\dfrac{v}{c})^2}$

Put the value into the formula

$l=1\times\sqrt{1-(\dfrac{\dfrac{1}{9}c^2}{c^2})}$

$l=1\times\sqrt{1-(\dfrac{1}{9})}$

$l=0.94\ m$

Hence, The length is 0.94 m